Probabilistic Methods for Dynamic Communication Networks

Publications

Articles in Refereed Journals

• C.F. Coletti, L.R. DE Lima, A. Hinsen, B. Jahnel, D.R. Valesin, Limiting shape for first-passage percolation models on random geometric graphs, Journal of Applied Probability, published online on 24.04.2023, DOI 10.1017/jpr.2023.5. .
  Abstract
  Let a random geometric graph be defined in the supercritical regime for the existence of a unique infinite connected component in Euclidean space. Consider the first-passage percolation model with independent and identically distributed random variables on the random infinite connected component. We provide sufficient conditions for the existence of the asymptotic shape and we show that the shape is an Euclidean ball. We give some examples exhibiting the result for Bernoulli percolation and the Richardson model. For the Richardson model we further show that it converges weakly to a branching process in the joint limit of large intensities and slow passing times.

• CH. Hirsch, B. Jahnel, E. Cali, Connection intervals in multi-scale infrastructure-augmented dynamic networks, Stochastic Models, published online on 06.03.2023, DOI 1080/15326349.2023.2184832 .
  Abstract
  We consider a hybrid spatial communication system in which mobile nodes can connect to static sinks in a bounded number of intermediate relaying hops. We describe the distribution of the connection intervals of a typical mobile node, i.e., the intervals of uninterrupted connection to the family of sinks. This is achieved in the limit of many hops, sparse sinks and growing time horizons. We identify three regimes illustrating that the limiting distribution depends sensitively on the scaling of the time horizon.

• N. Djurdjevac Conrad, J. Köppl, A. Djurdjevac, Feedback loops in opinion dynamics of agent-based models with multiplicative noise, Entropy. An International and Interdisciplinary Journal of Entropy and Information Studies, 24 (2022), pp. e24101352/1--e24101352/23, DOI 10.3390/e24101352 .
  Abstract
  We introduce an agent-based model for co-evolving opinion and social dynamics, under the influence of multiplicative noise. In this model, every agent is characterized by a position in a social space and a continuous opinion state variable. Agents? movements are governed by positions and opinions of other agents and similarly, the opinion dynamics is influenced by agents? spatial proximity and their opinion similarity. Using numerical simulations and formal analysis, we study this feedback loop between opinion dynamics and mobility of agents in a social space. We investigate the behavior of this ABM in different regimes and explore the influence of various factors on appearance of emerging phenomena such as group formation and opinion consensus. We study the empirical distribution and in the limit of infinite number of agents we derive a corresponding reduced model given by a partial differential equation (PDE). Finally, using numerical examples we show that a resulting PDE model is a good approximation of the original ABM.

• N. Engler, B. Jahnel, Ch. Külske, Gibbsianness of locally thinned random fields, Markov Processes and Related Fields, 28 (2022), pp. 185--214, DOI 10.48550/arXiv.2201.02651 .
  Abstract
  We consider the locally thinned Bernoulli field on ℤ ^d, which is the lattice version of the Type-I Matérn hardcore process in Euclidean space. It is given as the lattice field of occupation variables, obtained as image of an i.i.d. Bernoulli lattice field with occupation probability p, under the map which removes all particles with neighbors, while keeping the isolated particles. We prove that the thinned measure has a Gibbsian representation and provide control on its quasilocal dependence, both in the regime of small p, but also in the regime of large p, where the thinning transformation changes the Bernoulli measure drastically. Our methods rely on Dobrushin uniqueness criteria, disagreement percolation arguments [46], and cluster expansions

• CH. Hirsch, B. Jahnel, S. Muirhead, Sharp phase transition for Cox percolation, Electronic Communications in Probability, 27 (2022), pp. 48/1--48/13, DOI 10.1214/22-ECP487 .
  Abstract
  We prove the sharpness of the percolation phase transition for a class of Cox percolation models, i.e., models of continuum percolation in a random environment. The key requirements are that the environment has a finite range of dependence and satisfies a local boundedness condition, however the FKG inequality need not hold. The proof combines the OSSS inequality with a coarse-graining construction.

• S.K. Iyer, S.K. Jhawar, Phase transitions and percolation at criticality in enhanced random connection models, Mathematical Physics, Analysis and Geometry, 25 (2022), pp. 4/1--4/40, DOI 10.1007/s11040-021-09409-y .
  Abstract
  We study phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick model. These models are built on a homogeneous Poisson point process P?P? in R2R2 of intensity ?. In the homogeneous RCM, the vertices at x,y are connected with probability g( x ? y ), independent of everything else, where g:[0,?)?[0,1]g:[0,?)?[0,1] and ? is the Euclidean norm. In the inhomogeneous version of the model, points of P?P? are endowed with weights that are non-negative independent random variables with distribution P(W>w)=w??1[1,?)(w)P(W>w)=w??1[1,?)(w), ? >?0. Vertices located at x,y with weights Wx,Wy are connected with probability 1?exp(??WxWy x?y ?)1?exp?(??WxWy x?y ?), ?,? >?0, independent of all else. The graphs are enhanced by considering the edges of the graph as straight line segments starting and ending at points of P?P?. A path in the graph is a continuous curve that is a subset of the union of all these line segments. The Poisson stick model consists of line segments of independent random lengths and orientation with the mid point of each segment located at a distinct point of P?P?. Intersecting lines form a path in the graph. A graph is said to percolate if there is an infinite connected component or path. We derive conditions for the existence of a phase transition and show that there is no percolation at criticality.

• B. Jahnel, Ch. Hirsch, E. Cali, Percolation and connection times in multi-scale dynamic networks, Stochastic Processes and their Applications, 151 (2022), pp. 490--518, DOI 10.1016/j.spa.2022.06.008 .
  Abstract
  We study the effects of mobility on two crucial characteristics in multi-scale dynamic networks: percolation and connection times. Our analysis provides insights into the question, to what extent long-time averages are well-approximated by the expected values of the corresponding quantities, i.e., the percolation and connection probabilities. In particular, we show that in multi-scale models, strong random effects may persist in the limit. Depending on the precise model choice, these may take the form of a spatial birth-death process or a Brownian motion. Despite the variety of structures that appear in the limit, we show that they can be tackled in a common framework with the potential to be applicable more generally in order to identify limits in dynamic spatial network models going beyond the examples considered in the present work.

• B. Jahnel, A. Tóbiás, E. Cali, Phase transitions for the Boolean model of continuum percolation for Cox point processes, Brazilian Journal of Probability and Statistics, 3 (2022), pp. 20--44, DOI 10.1214/21-BJPS514 .
  Abstract
  We consider the Boolean model with random radii based on Cox point processes. Under a condition of stabilization for the random environment, we establish existence and non-existence of subcritical regimes for the size of the cluster at the origin in terms of volume, diameter and number of points. Further, we prove uniqueness of the infinite cluster for sufficiently connected environments.

• B. Jahnel, A. Tóbiás, Absence of percolation in graphs based on stationary point processes with degrees bounded by two, Random Structures and Algorithms, 62 (2022), pp. 240--255, DOI 10.1002/rsa.21084 .
  Abstract
  We consider undirected graphs that arise as deterministic functions of stationary point processes such that each point has degree bounded by two. For a large class of point processes and edge-drawing rules, we show that the arising graph has no infinite connected component, almost surely. In particular, this extends our previous result for SINR graphs based on stabilizing Cox point processes and verifies the conjecture of Balister and Bollobás that the bidirectional $k$-nearest neighbor graph of a two-dimensional homogeneous Poisson point process does not percolate for k=2.

• B. Jahnel, A. Tóbiás, SINR percolation for Cox point processes with random powers, Adv. Appl. Math., 54 (2022), pp. 227--253, DOI 10.1017/apr.2021.25 .
  Abstract
  Signal-to-interference plus noise ratio (SINR) percolation is an infinite-range dependent variant of continuum percolation modeling connections in a telecommunication network. Unlike in earlier works, in the present paper the transmitted signal powers of the devices of the network are assumed random, i.i.d. and possibly unbounded. Additionally, we assume that the devices form a stationary Cox point process, i.e., a Poisson point process with stationary random intensity measure, in two or higher dimensions. We present the following main results. First, under suitable moment conditions on the signal powers and the intensity measure, there is percolation in the SINR graph given that the device density is high and interferences are sufficiently reduced, but not vanishing. Second, if the interference cancellation factor γ and the SINR threshold τ satisfy γ ≥ 1/(2τ), then there is no percolation for any intensity parameter. Third, in the case of a Poisson point process with constant powers, for any intensity parameter that is supercritical for the underlying Gilbert graph, the SINR graph also percolates with some small but positive interference cancellation factor.

Contributions to Collected Editions

• B. Jahnel, A.J. Tóbiás, Absence of percolation in graphs based on stationary point processes with degrees bounded by two (extended abstract), in: Proceedings of the 12th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications, T. Jordán, G.Y. Katona, C. Király, G. Wiener, eds., 613 of the 12th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications, BME VIK Számítástudományi és Információelméleti Tanszék, 2023, pp. 537--542.

• Z. Benomar, Ch. Ghribi, E. Cali, A. Hinsen, B. Jahnel, Agent-based modeling and simulation for malware spreading in D2D networks, AAMAS '22: Proceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems, Auckland, New Zealand, May 11 - 13, 2022, International Foundation for Autonomous Agents and Multiagent Systems, Richland, SC, 2022, pp. 91--99.
  Abstract
  This paper presents a new multi-agent model for simulating malware propagation in device-to-device (D2D) 5G networks. This model allows to understand and analyze mobile malware-spreading dynamics in such highly dynamical networks. Additionally, we present a theoretical study to validate and benchmark our proposed approach for some basic scenarios that are less complicated to model mathematically and also to highlight the key parameters of the model. Our simulations identify critical thresholds for em no propagation and for em maximum malware propagation and make predictions on the malware-spread velocity as well as device-infection rates. To the best of our knowledge, this paper is the first study applying agent-based simulations for malware propagation in D2D.

• CH. Ghribi, E. Cali, Ch. Hirsch, B. Jahnel, Agent-based simulations for coverage extensions in 5G networks and beyond, in: 2022 25th Conference on Innovation in Clouds, Internet and Networks (ICIN), M.F. Zhani, N. Limam, P. Borylo, A. Boubendir, C.R.P. Dos Santos, eds., IEEE, 2022, pp. 1--7, DOI 10.1109/ICIN53892.2022.9758136 .

Preprints, Reports, Technical Reports

• B. Jahnel, J. Köppl, Trajectorial dissipation of $Phi$-entropies for interacting particle systems, Preprint no. 3019, WIAS, Berlin, 2023, DOI 10.20347/WIAS.PREPRINT.3019 .
  Abstract, PDF (300 kByte)
  A classical approach for the analysis of the longtime behavior of Markov processes is to consider suitable Lyapunov functionals like the variance or more generally Φ -entropies. Via purely analytic arguments it can be shown that these functionals are indeed non-increasing in time under quite general assumptions on the process. We complement these classical results via a more probabilistic approach and show that dissipation is already present on the level of individual trajectories for spatially-extended systems of infinitely many interacting particles with arbitrary underlying geometry and compact local spin spaces. This extends previous results from the setting of finite-state Markov chains or diffusions in Rⁿ to an infinite-dimensional setting with weak assumptions on the dynamics.

• P. Gracar, L. Lüchtrath, Ch. Mönch, The emergence of a giant component in one-dimensional inhomogeneous networks with long-range effects, Preprint no. 3011, WIAS, Berlin, 2023, DOI 10.20347/WIAS.PREPRINT.3011 .
  Abstract, PDF (5064 kByte)
  We study the weight-dependent random connection model, a class of sparse graphs featuring many real-world properties such as heavy-tailed degree distributions and clustering. We introduce a coefficient, (deltaf), measuring the effect of the degree-distribution on the occurrence of long edges. We identify a sharp phase transition in (deltaf) for the existence of a giant component in dimension (d=1).

• B. Jahnel, J. Köppl, On the long-time behaviour of reversible interacting particle systems in one and two dimensions, Preprint no. 3004, WIAS, Berlin, 2023, DOI 10.20347/WIAS.PREPRINT.3004 .
  Abstract, PDF (287 kByte)
  By refining Holley's free energy technique, we show that, under quite general assumptions on the dynamics, the attractor of a (possibly non-translation-invariant) interacting particle system in one or two spatial dimensions is contained in the set of Gibbs measures if the dynamics admits a reversible Gibbs measure. In particular, this implies that there can be no reversible interacting particle system that exhibits time-periodic behaviour and that every reversible interacting particle system is ergodic if and only if the reversible Gibbs measure is unique. In the special case of non-attractive stochastic Ising models this answers a question due to Liggett.

• B. Jahnel, L. Lüchtrath, Existence of subcritical percolation phases for generalised weight-dependent random connection models, Preprint no. 2993, WIAS, Berlin, 2023, DOI 10.20347/WIAS.PREPRINT.2993 .
  Abstract, PDF (299 kByte)
  We derive a sufficient condition for the existence of a subcritical percolation phase for a wide range of continuum percolation models where each vertex is embedded into Euclidean space and carries an independent weight. In contrast to many established models, the presence of an edge is not only allowed to depend on the distance and weights of its end vertices but can also depend on the surrounding vertex set. Our result can be applied in particular to models combining heavy-tailed degree distributions and long-range effects, which are typically well connected. Moreover, we establish bounds on the tail-distribution of the number of points and the diameter of the subcritical component of a typical point. The proofs rest on a multi-scale argument.

• A. Hinsen, B. Jahnel, E. Cali, J.-P. Wary, Chase-escape in dynamic device-to-device networks, Preprint no. 2969, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2969 .
  Abstract, PDF (1550 kByte)
  The present paper features results on global survival and extinction of an infection in a multi-layer network of mobile agents. Expanding on a model first presented in CHJW22, we consider an urban environment, represented by line-segments in the plane, in which agents move according to a random waypoint model based on a Poisson point process. Whenever two agents are at sufficiently close proximity for a sufficiently long time the infection can be transmitted and then propagates into the system according to the same rule starting from a typical device. Inspired by wireless network architectures, the network is additionally equipped with a second class of agents that is able to transmit a patch to neighboring infected agents that in turn can further distribute the patch, leading to a chase-escape dynamics. We give conditions for parameter configurations that guarantee existence and absence of global survival as well as an in-and-out of the survival regime, depending on the speed of the devices. We also provide complementary results for the setting in which the chase-escape dynamics is defined as an independent process on the connectivity graph. The proofs mainly rest on percolation arguments via discretization and multiscale analysis.

• Z. Benomar, Ch. Ghribi, E. Cali, A. Hinsen, B. Jahnel, J.-P. Wary, Multi-agent simulations for virus propagation in D2D 5G+ networks, Preprint no. 2953, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2953 .
  Abstract, PDF (367 kByte)
  In this paper we present results for an extended class of multi-agent simulation models for malware propagation in device-to-device 5G networks, first exhibited in citeAgentBasedAAMAS. The models allow to understand and analyze mobile malware spreading dynamics in highly dynamical networks and also to assess the effectiveness of a proposed counter measure policy for reversing attacks and securing the system. Our main simulation studies identify critical thresholds for maximal malware propagation and isolate two distinguished regimes for malware survival and extermination depending on a variety of parameters. We further predict via simulations the malware spreading velocities, depending on device density and speed, as well as the percentage of counter agents that have to be introduced into the network for malware elimination. We complement these findings and state also an associated theoretical study that highlights the key parameters of our agent-based model and exhibit certain linear relationships between them [1].

• A. Hinsen, B. Jahnel, E. Cali, J.-P. Wary, Connectivity in mobile device-to-device networks in urban environments, Preprint no. 2952, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2952 .
  Abstract, PDF (606 kByte)
  In this article we setup a dynamic device-to-device communication system where devices, given as a Poisson point process, move in an environment, given by a street system of random planar-tessellation type, via a random-waypoint model. Every device independently picks a target location on the street system using a general waypoint kernel, and travels to the target along the shortest path on the streets with an individual velocity. Then, any pair of devices becomes connected whenever they are on the same street in sufficiently close proximity, for a sufficiently long time. After presenting some general properties of the multi-parameter system, we focus on an analysis of the clustering behavior of the random connectivity graph. In our main results we isolate regimes for the almost-sure absence of percolation if, for example, the device intensity is too small, or the connectivity time is too large. On the other hand, we exhibit parameter regimes of sufficiently large intensities of devices, under favorable choices of the other parameters, such that percolation is possible with positive probability. Most interestingly, we also show an in-and-out of percolation as the velocity increases. The rigorous analysis of the system mainly rests on comparison arguments with simplified models via spatial coarse graining and thinning approaches. Here we also make contact to geostatistical percolation models with infinite-range dependencies.

• B. Jahnel, S.K. Jhawar, A.D. Vu, Continuum percolation in a nonstabilizing environment, Preprint no. 2943, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2943 .
  Abstract, PDF (2463 kByte)
  We prove nontrivial phase transitions for continuum percolation in a Boolean model based on a Cox point process with nonstabilizing directing measure. The directing measure, which can be seen as a stationary random environment for the classical Poisson--Boolean model, is given by a planar rectangular Poisson line process. This Manhattan grid type construction features long-range dependencies in the environment, leading to absence of a sharp phase transition for the associated Cox--Boolean model. Our proofs rest on discretization arguments and a comparison to percolation on randomly stretched lattices established in [MR2116736].

• B. Jahnel, J. Köppl, Dynamical Gibbs variational principles for irreversible interacting particle systems with applications to attractor properties, Preprint no. 2935, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2935 .
  Abstract, PDF (355 kByte)
  We consider irreversible translation-invariant interacting particle systems on the d-dimensional cubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy conditions on the rates and the specification we prove, that zero relative entropy loss of a translation-invariant measure implies, that the measure is Gibbs w.r.t. the same specification as the time-stationary Gibbs measure. As an application, we obtain the attractor property for irreversible interacting particle systems, which says that any weak limit point of any trajectory of translation-invariant measures is a Gibbs measure w.r.t. the same specification as the time-stationary measure. This extends previously known results to fairly general irreversible interacting particle systems.

• CH. Ghribi, E. Cali, Ch. Hirsch, B. Jahnel, Agent-based simulations for coverage extensions in 5G networks and beyond, Preprint no. 2920, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2920 .
  Abstract, PDF (1032 kByte)
  Device-to-device (D2D) communications is one of the key emerging technologies for the fifth generation (5G) networks and beyond. It enables direct communication between mobile users and thereby extends coverage for devices lacking direct access to the cellular infrastructure and hence enhances network capacity. D2D networks are complex, highly dynamic and will be strongly augmented by intelligence for decision making at both the edge and core of the network, which makes them particularly difficult to predict and analyze. Conventionally, D2D systems are evaluated, investigated and analyzed using analytical and probabilistic models (e.g., from stochastic geometry). However, applying classical simulation and analytical tools to such a complex system is often hard to track and inaccurate. In this paper, we present a modeling and simulation framework from the perspective of complex-systems science and exhibit an agent-based model for the simulation of D2D coverage extensions. We also present a theoretical study to benchmark our proposed approach for a basic scenario that is less complicated to model mathematically. Our simulation results show that we are indeed able to predict coverage extensions for multi-hop scenarios and quantify the effects of street-system characteristics and pedestrian mobility on the connection time of devices to the base station (BS). To our knowledge, this is the first study that applies agent-based simulations for coverage extensions in D2D.

• Z. Benomar, Ch. Ghribi, E. Cali, A. Hinsen, B. Jahnel, Agent-based modeling and simulation for malware spreading in D2D networks, Preprint no. 2919, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2919 .
  Abstract, PDF (286 kByte)
  This paper presents a new multi-agent model for simulating malware propagation in device-to-device (D2D) 5G networks. This model allows to understand and analyze mobile malware-spreading dynamics in such highly dynamical networks. Additionally, we present a theoretical study to validate and benchmark our proposed approach for some basic scenarios that are less complicated to model mathematically and also to highlight the key parameters of the model. Our simulations identify critical thresholds for em no propagation and for em maximum malware propagation and make predictions on the malware-spread velocity as well as device-infection rates. To the best of our knowledge, this paper is the first study applying agent-based simulations for malware propagation in D2D.

• O. Collin, B. Jahnel, W. König, The free energy of a box-version of the interacting Bose gas, Preprint no. 2914, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2914 .
  Abstract, PDF (1441 kByte)
  The interacting quantum Bose gas is a random ensemble of many Brownian bridges (cycles) of various lengths with interactions between any pair of legs of the cycles. It is one of the standard mathematical models in which a proof for the famous Bose--Einstein condensation phase transition is sought for. We introduce a simplified version of the model with an organisation of the particles in deterministic boxes instead of Brownian cycles as the marks of a reference Poisson point process (for simplicity, in Z ^d, instead of R ^d). We derive an explicit and interpretable variational formula in the thermodynamic limit for the limiting free energy of the canonical ensemble for any value of the particle density. This formula features all relevant physical quantities of the model, like the microscopic and the macroscopic particle densities, together with their mutual and self-energies and their entropies. The proof method comprises a two-step large-deviation approach for marked Poisson point processes and an explicit distinction into small and large marks. In the characteristic formula, each of the microscopic particles and the statistics of the macroscopic part of the configuration are seen explicitly; the latter receives the interpretation of the condensate. The formula enables us to prove a number of properties of the limiting free energy as a function of the particle density, like differentiability and explicit upper and lower bounds, and a qualitative picture below and above the critical threshold (if it is finite). This proves a modified saturation nature of the phase transition. However, we have not yet succeeded in proving the existence of this phase transition.

Talks, Poster

• B. Jahnel, Continuum percolation in random environments, Topics in High Dimensional Probability, January 2 - 13, 2023, International Centre for Theoretical Sciences, Bangalore, India, January 3, 2023.

• S.K. Jhawar, Poisson approximation and connectivity in a scale-free network, Spring School on Random geometric graphs, March 28 - April 1, 2022, Technische Universität Darmstadt, Fachbereich Mathematik, March 31, 2022.

• S.K. Jhawar, Poisson approximation and connectivity in a scale-free network, SPP Workshop on Limit Theorems for Spatial Random Structures, September 7 - 9, 2022, Ruhr University Bochum, September 8, 2022.

• J. Köppl, Dynamical Gibbs variational principles for irreversible interacting particle systems and applications to attractor properties, DMV Annual Meeting 2022, Section 12: ``Probability, Computational Stochastics, and Financial Mathematics'', September 12 - 16, 2022, Freie Universität Berlin, September 15, 2022.

• J. Köppl, Dynamical Gibbs variational principles for irreversible interacting particle systems and applications to attractor properties, BMS--BGSMath JUNIOR MEETING 2022, September 5 - 7, 2022, Universitat de Barcelona, Spain, October 6, 2022.

• J. Köppl, Dynamical Gibbs variational principles for irreversible interacting particle systems with applications to attractor properties, DIES Matematicus, November 25, 2022, Technische Universität Berlin, Institut für Mathematik, November 25, 2022.

• A.D. Vu, An Application for Percolation Theory in Analysis, Spring School on Random geometric graphs, March 28 - April 1, 2022, Technische Universität Darmstadt, Fachbereich Mathematik, March 31, 2022.

• A.D. Vu, Existence of Infinite Cluster on the Manhattan Grid, Processes on Random Geometric Graphs, September 12 - 16, 2022, Universität zu Köln, Mathematisches Institut.

• A.D. Vu, Nontrivial Phase Transition on the Manhattan Grid, Workshop ``Recent Trends in Spatial Stochastic Processes'', October 3 - 7, 2022, Workshop Centre in the area of Stochastics (EURANDOM), Eindhoven, Netherlands.

• A.D. Vu, Percolation theory and the effective conductivity, 21st Workshop on Stochastic Geometry, Stereology and Image Analysis, June 5 - 10, 2022, Nesuchyne, Czech Republic, June 6, 2022.

• A.D. Vu, Stochastic Homogenization on Irregularly Perforated Domains (online talk), SIAM 2022 Conference on Analysis of Partial Differential Equations (PD22) (Online Event), March 14 - 18, 2022, Virtual Conference --- Originally scheduled in Berlin, Germany, null.

• B. Jahnel, Continuum Percolation in Random Environments (Part 1), Stochastic modelling in the life science: From evolution to medicine, August 1 - 3, 2022, Hausdorff Center for Mathematics, Universität Bonn, August 1, 2022.

• B. Jahnel, Continuum Percolation in Random Environments (Part 2), Stochastic modelling in the life science: From evolution to medicine, August 1 - 3, 2022, Hausdorff Center for Mathematics, Universität Bonn, August 2, 2022.

• B. Jahnel, Die Poesie der Logik, Dedekinder Orientierungswoche im Wintersemester 2022/23, Technische Universität Braunschweig, Institut für Mathematische Stochastik, October 20, 2022.

• B. Jahnel, First-passage percolation and chase-escape dynamics on random geometric graphs, Spring School on Random Geometric Graphs, March 28 - April 1, 2022, Technische Universität Darmstadt, Fachbereich Mathematik, March 30, 2022.

• B. Jahnel, Malware propagation in mobile device-to-device networks (online talk), Joint H2020 AI@EDGE and INSPIRE-5G Project Workshop (Online Event), Workshop of the IEEE International Conference on Cloud Networking, Nov. 7--10, 2022, Paris, France, November 8 - 9, 2022, November 8, 2022.

• B. Jahnel, Phase transitions and large deviations for the Boolean model of continuum percolation for Cox point processes (online talk), Probability Seminar University Padua, Università di Padova, Dipartimento di Matematica, Italy, March 25, 2022.

• B. Jahnel, Stochastic geometry for telecommunications, Leibniz MMS Days 2022, April 25 - 27, 2022, Potsdam-Institut für Klimafolgenforschung (PIK), April 26, 2022.

External Preprints

• N. Djurdjevac Conrad, J. Köppl, A. Djurdjevac, Feedback loops in opinion dynamics of agent-based models with multiplicative noise, Preprint no. arXiv:2209.07151, Cornell University, 2022, DOI 10.48550/arXiv.2209.07151 .
  Abstract
  We introduce an agent-based model for co-evolving opinion and social dynamics, under the influence of multiplicative noise. In this model, every agent is characterized by a position in a social space and a continuous opinion state variable. Agents? movements are governed by positions and opinions of other agents and similarly, the opinion dynamics is influenced by agents? spatial proximity and their opinion similarity. Using numerical simulations and formal analysis, we study this feedback loop between opinion dynamics and mobility of agents in a social space. We investigate the behavior of this ABM in different regimes and explore the influence of various factors on appearance of emerging phenomena such as group formation and opinion consensus. We study the empirical distribution and in the limit of infinite number of agents we derive a corresponding reduced model given by a partial differential equation (PDE). Finally, using numerical examples we show that a resulting PDE model is a good approximation of the original ABM.

• P. Gracar, L. Lüchtrath, Ch. Mönch, Finiteness of the percolation threshold for inhomogeneous long-range models in one dimension, Preprint no. arXiv:2203.11966, Cornell University, 2022, DOI 10.48550/arXiv.2203.11966 .
  Abstract
  We consider a large class of inhomogeneous spatial random graphs on the real line. Each vertex carries an i.i.d. weight and edges are drawn such that short edges and edges to vertices with large weights are preferred. This allows the study of models with long-range effects and heavy-tailed degree distributions. We introduce a new coefficient, ?eff, measuring the influence of the degree-distribution on the long-range edges. We identify a sharp phase transition in ?eff for the existence of a supercritical percolation phase. In Gracar, Lüchtrath, Mörters 2021, it is shown that the soft Boolean model and the age-dependent random connection model are examples for models that have parameter regimes where there is no subcritical percolation phase. This paper completes these results and shows that in dimension one there exist parameter regimes in which the models have no supercritical phase and regimes with both super- and a subcritical phases.