Large deviations and wandering exponent for random walk in a dynamic beta environment
Probability
2021-03-17 v2
Abstract
Random walk in a dynamic i.i.d. beta random environment, conditioned to escape at an atypical velocity, converges to a Doob transform of the original walk. The Doob-transformed environment is correlated in time, i.i.d. in space, and its marginal density function is a product of a beta density and a hypergeometric function. Under its averaged distribution the transformed walk obeys the wandering exponent 2/3 that agrees with Kardar-Parisi-Zhang universality. The harmonic function in the Doob transform comes from a Busemann-type limit and appears as an extremal in a variational problem for the quenched large deviation rate function.
Cite
@article{arxiv.1801.08070,
title = {Large deviations and wandering exponent for random walk in a dynamic beta environment},
author = {Márton Balázs and Firas Rassoul-Agha and Timo Seppäläinen},
journal= {arXiv preprint arXiv:1801.08070},
year = {2021}
}
Comments
47 pages, 6 figures. Some proofs were shortened with references to the concurrent paper arXiv:1711.08432