Averaged vs. quenched large deviations and entropy for random walk in a dynamic random environment
Abstract
We consider random walk with bounded jumps on a hypercubic lattice of arbitrary dimension in a dynamic random environment. The environment is temporally independent and spatially translation invariant. We study the rate functions of the level-3 averaged and quenched large deviation principles from the point of view of the particle. In the averaged case the rate function is a specific relative entropy, while in the quenched case it is a Donsker-Varadhan type relative entropy for Markov processes. We relate these entropies to each other and seek to identify the minimizers of the level-3 to level-1 contractions in both settings. Motivation for this work comes from variational descriptions of the quenched free energy of directed polymer models where the same Markov process entropy appears.
Cite
@article{arxiv.1607.07000,
title = {Averaged vs. quenched large deviations and entropy for random walk in a dynamic random environment},
author = {Firas Rassoul-Agha and Timo Seppäläinen and Atilla Yilmaz},
journal= {arXiv preprint arXiv:1607.07000},
year = {2016}
}
Comments
38 pages