2018/08/31 by Francesco Coghi, Jules Morand, Hugo Touchette
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Combinatorics #Entropy (arrow of time) #Heterogeneous random walk in one dimension #Large deviations theory #Logarithm #Mathematical analysis #Mathematics #Observable #Physics #Quantum mechanics #Random walk #Statistical Mechanics and Entropy #Statistical physics #Statistics #Trajectory #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.99.022137
published as Phys. Rev. E 99, 022137 (2019) · v1: 12 pages, 8 figures. v2: minor typos corrected. v3: minor typos, close to published version
arxiv created 2019/02/20 · openalex publication_date 2019/02/26 · arxiv updated 2019/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study the rare fluctuations or large deviations of time-integrated functionals or observables of an unbiased random walk evolving on Erdös-Rényi 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, similar 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.