Open Access
2017 Averaged vs. quenched large deviations and entropy for random walk in a dynamic random environment
Firas Rassoul-Agha, Timo Seppäläinen, Atilla Yilmaz
Electron. J. Probab. 22: 1-47 (2017). DOI: 10.1214/17-EJP74


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.


Download Citation

Firas Rassoul-Agha. Timo Seppäläinen. Atilla Yilmaz. "Averaged vs. quenched large deviations and entropy for random walk in a dynamic random environment." Electron. J. Probab. 22 1 - 47, 2017.


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

zbMATH: 1368.60028
MathSciNet: MR3672833
Digital Object Identifier: 10.1214/17-EJP74

Primary: 60F10 , 60K37 , 82C41 , 82C44

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

Vol.22 • 2017
Back to Top