Articles in Refereed Journals

  • CH. Hirsch, B. Jahnel, P. Keeler, R.I.A. Patterson, Large deviations in relay-augmented wireless networks, Queueing Systems. Theory and Applications, pp. published online on 28.10.2017, url, DOI 10.1007/s11134-017-9555-9 .
    We analyze a model of relay-augmented cellular wireless networks. The network users, who move according to a general mobility model based on a Poisson point process of continuous trajectories in a bounded domain, try to communicate with a base station located at the origin. Messages can be sent either directly or indirectly by relaying over a second user. We show that in a scenario of an increasing number of users, the probability that an atypically high number of users experiences bad quality of service over a certain amount of time, decays at an exponential speed. This speed is characterized via a constrained entropy minimization problem. Further, we provide simulation results indicating that solutions of this problem are potentially non-unique due to symmetry breaking. Also two general sources for bad quality of service can be detected, which we refer to as isolation and screening.

  • CH. Hirsch, B. Jahnel, P. Keeler, R.I.A. Patterson, Traffic flow densities in large transport networks, Advances in Applied Probability, 49 (2017), pp. 1091--1115, DOI 10.1017/apr.2017.35 .
    We consider transport networks with nodes scattered at random in a large domain. At certain local rates, the nodes generate traffic flowing according to some navigation scheme in a given direction. In the thermodynamic limit of a growing domain, we present an asymptotic formula expressing the local traffic flow density at any given location in the domain in terms of three fundamental characteristics of the underlying network: the spatial intensity of the nodes together with their traffic generation rates, and of the links induced by the navigation. This formula holds for a general class of navigations satisfying a link-density and a sub-ballisticity condition. As a specific example, we verify these conditions for navigations arising from a directed spanning tree on a Poisson point process with inhomogeneous intensity function.

  • B. Jahnel, Ch. Külske, The Widom--Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality, The Annals of Applied Probability, 27 (2017), pp. 3845--3892, DOI 10.1214/17-AAP1298 .
    We consider the continuum Widom-Rowlinson model under independent spin-flip dynamics and investigate whether and when the time-evolved point process has an (almost) quasilocal specification (Gibbs-property of the time-evolved measure). Our study provides a first analysis of a Gibbs-non-Gibbs transition for point particles in Euclidean space. We find a picture of loss and recovery, in which even more regularity is lost faster than it is for time-evolved spin models on lattices. We show immediate loss of quasilocality in the percolation regime, with full measure of discontinuity points for any specification. For the color-asymmetric percolating model, there is a transition from this non-a.s. quasilocal regime back to an everywhere Gibbsian regime. At the sharp reentrance time tG > 0 the model is a.s. quasilocal. For the colorsymmetric model there is no reentrance. On the constructive side, for all t > tG , we provide everywhere quasilocal specifications for the time-evolved measures and give precise exponential estimates on the influence of boundary conditions.

Talks, Poster

  • B. Jahnel, Fabrics of dreams, Seminar am Ökonomischen Institut, Johannes Gutenberg Universität Mainz, Ökonomisches Institut, April 26, 2017.

  • B. Jahnel, The Widom--Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality, Oberseminar Wahrscheinlichkeitstheorie, Ludwig-Maximilians-Universität München, Fakultät für Mathematik, Informatik und Statistik, February 13, 2017.

  • B. Jahnel, The Widom--Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality, Westfälische Wilhelms-Universität Münster, Fachbereich Mathematik und Informatik, January 18, 2017.

  • B. Jahnel, The Widom--Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality, Oberseminar Stochastik, Johannes Gutenberg Universität Mainz, Institut für Mathematik, April 25, 2017.

  • B. Jahnel, The Widom-Rowlinson model under spin flip: immediate loss and sharp recovery of quasilocality, Université du Luxembourg, Faculté des Sciences, de la Technologie et de la Communication (FSTC), Luxembourg, March 3, 2017.

  • P. Keeler, Optimizing spatial throughput in device-to-device networks, Applied Probability @ The Rock -- An International Workshop celebrating Phil Pollett's 60th Birthday, April 17 - 21, 2017, University of Adelaide, School of Mathematical Sciences, Uluru, Australia, April 20, 2017.