Large and moderate deviations in Poisson navigations

Autor:	Ghosh, Partha Pratim, Jahnel, Benedikt, Jhawar, Sanjoy Kumar
Rok vydání:	2024
Předmět:	Mathematics - Probability 60D05 60G70 60G55 05C80
Druh dokumentu:	Working Paper
Popis:	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 horizontal displacement as well as renewal-process arguments. Comment: 22 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.14295 Zobrazit plný text záznamu View this record from Arxiv