WIAS Preprint No. 3096, (2024)
Large and moderate deviations in Poisson navigations
Authors
- Ghosh, Partha Pratim
- Jahnel, Benedikt
ORCID: 0000-0002-4212-0065 - Jhawar, Sanjoy Kumar
ORCID: 0000-0003-1297-0525
2020 Mathematics Subject Classification
- 60D05 60G70 60G55 05C80
Keywords
- Traffic network, directed-navigation, Poisson point process, renewal process, moderate-deviation principle, large-deviation principle
DOI
Abstract
We derive large- and moderate-deviation results in random networks given as planar directed navigations on homogeneous Poisson point processes. In this non-Markovian routing scheme, starting from the origin, at each consecutive step a Poisson point is joined by an edge to its nearest Poisson point to the right within a cone. We establish precise exponential rates of decay for the probability that the vertical displacement of the random path is unexpectedly large. The proofs rest on controlling the dependencies of the individual steps and the randomness in the horizonal displacement as well as renewal-process arguments.
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