Averaged vs. quenched large deviations and entropy for random walk in a dynamic random environment

2016/07/24 by Firas Rassoul-Agha, Rassoul-Agha, Firas, Timo Seppäläinen +3
Mathematics · #60F10 (Primary) 82C41 #60K37 #82C44 (Secondary) #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F10 #msc:60K37 #msc:82C41 #msc:82C44

paper · pdf · doi:10.48550/arxiv.1607.07000

38 pages

arxiv created 2016/07/24 · arxiv updated 2016/07/26

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.

Related

• Quenched Free Energy and Large Deviations for Random Walks in Random Potentials
• Quenched large deviations for multidimensional random walk in random environment: a variational formula
• Level 1 quenched large deviation principle for random walk in dynamic random environment
• Quenched Point-to-Point Free Energy for Random Walks in Random Potentials
• Quenched large deviations for random walk in a random environment