Electronic Journal of Probability

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

Firas Rassoul-Agha, Timo Seppäläinen, and Atilla Yilmaz

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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
Received: 24 July 2016
Accepted: 1 June 2017
First available in Project Euclid: 6 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1499306456

Digital Object Identifier
doi:10.1214/17-EJP74

Mathematical Reviews number (MathSciNet)
MR3672833

Zentralblatt MATH identifier
1368.60028

Subjects
Primary: 60K37: Processes in random environments 60F10: Large deviations 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50] 82C44: Dynamics of disordered systems (random Ising systems, etc.)

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

Rights
Creative Commons Attribution 4.0 International License.

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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