Random walks on quasi one dimensional lattices: large deviations and fluctuation theorems
Abstract
Several stochastic processes modeling molecular motors on a linear track are given by random walks (not necessarily Markovian) on quasi 1d lattices and share a common regenerative structure. Analyzing this abstract common structure, we derive information on the large fluctuations of the stochastic process by proving large deviation principles for the first--passage times and for the position. We focus our attention on the Gallavotti-Cohen-type symmetry of the position rate function (fluctuation theorem), showing its equivalence with the independence of suitable random variables. In the special case of Markov random walks, we show that this symmetry is universal only inside a suitable class of quasi 1d lattices.
Cite
@article{arxiv.1401.2256,
title = {Random walks on quasi one dimensional lattices: large deviations and fluctuation theorems},
author = {Alessandra Faggionato and Vittoria Silvestri},
journal= {arXiv preprint arXiv:1401.2256},
year = {2014}
}
Comments
37 pages, 3 figures. Replaced version: the part concerning LLN and invariance principle has been moved to http://arxiv.org/abs/1405.1214. Added Theorem 3. The new version concerns only large deviations and fluctuation theorems. Changed title,abstract, introduction