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

作者：Rassoul Agha Firas^*; Seppalainen Timo; Yilmaz Atilla

来源：Electronic Journal of Probability, 2017, 22(0): 57.

DOI：10.1214/17-EJP74

• random walk
• dynamic random environment
• large deviations
• averaged
• quenched
• empirical process
• Donsker-Varadhan relative entropy
• specific relative entropy
• Doob h-transform
• nonstationary process

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.

• 出版日期2017