## Electronic Journal of Probability

### 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.

#### Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 57, 47 pp.

Dates
Accepted: 1 June 2017
First available in Project Euclid: 6 July 2017

https://projecteuclid.org/euclid.ejp/1499306456

Digital Object Identifier
doi:10.1214/17-EJP74

Mathematical Reviews number (MathSciNet)
MR3672833

Zentralblatt MATH identifier
1368.60028

#### Citation

Rassoul-Agha, Firas; Seppäläinen, Timo; Yilmaz, Atilla. Averaged vs. quenched large deviations and entropy for random walk in a dynamic random environment. Electron. J. Probab. 22 (2017), paper no. 57, 47 pp. doi:10.1214/17-EJP74. https://projecteuclid.org/euclid.ejp/1499306456

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