Quenched Free Energy and Large Deviations for Random Walks in Random Potentials
Article first published online: 6 AUG 2012
Copyright © 2012 Wiley Periodicals, Inc.
Communications on Pure and Applied Mathematics
Volume 66, Issue 2, pages 202–244, February 2013
How to Cite
Rassoul-Agha, F., Seppäläinen, T. and Yilmaz, A. (2013), Quenched Free Energy and Large Deviations for Random Walks in Random Potentials. Comm. Pure Appl. Math., 66: 202–244. doi: 10.1002/cpa.21417
- Issue published online: 28 NOV 2012
- Article first published online: 6 AUG 2012
- Manuscript Revised: NOV 2011
- Manuscript Received: APR 2011
We study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can be unbounded and can depend on a few steps of the walk. Directed, undirected, and stretched polymers, as well as random walk in random environment, are covered. The restriction needed is on the moment of the potential, in relation to the degree of mixing of the ergodic environment. We derive two variational formulas for the limiting quenched free energy and prove a process-level quenched large deviation principle (LDP) for the empirical measure. As a corollary we obtain LDPs for types of random walks in random environments not covered by earlier results. © 2012 Wiley Periodicals, Inc.