Large deviations of random walks on random graphs
Abstract
We study using large deviation theory the fluctuations of time-integrated functionals or observables of the unbiased random walk evolving on Erd\"os-R\'enyi random graphs, and construct a modified, biased random walk that explains how these fluctuations arise in the long-time limit. Two observables are considered: the sum of the degrees visited by the random walk and the sum of their logarithm, related to the trajectory entropy. The modified random walk is used for both quantities to explain how sudden changes in degree fluctuations, akin to dynamical phase transitions, are related to localization transitions. For the second quantity, we also establish links between the large deviations of the trajectory entropy and the maximum entropy random walk.
Cite
@article{arxiv.1808.00700,
title = {Large deviations of random walks on random graphs},
author = {Francesco Coghi and Jules Morand and Hugo Touchette},
journal= {arXiv preprint arXiv:1808.00700},
year = {2019}
}
Comments
v1: 12 pages, 8 figures. v2: minor typos corrected. v3: minor typos, close to published version