期刊
PROBABILITY THEORY AND RELATED FIELDS
卷 158, 期 3-4, 页码 711-750出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00440-013-0494-z
关键词
Point-to-point; Quenched; Free energy; Large deviation; Random walk; Random environment; Polymer; Random potential; RWRE; RWRP; Directed polymer; Stretched polymer; Entropy; Variational formula
资金
- NSF [DMS-0747758, DMS-1003651]
- Wisconsin Alumni Research Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1003651] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0747758] Funding Source: National Science Foundation
We consider a random walk in a random potential on a square lattice of arbitrary dimension. The potential is a function of an ergodic environment and steps of the walk. The potential is subject to a moment assumption whose strictness is tied to the mixing of the environment, the best case being the i.i.d. environment. We prove that the infinite volume quenched point-to-point free energy exists and has a variational formula in terms of entropy. We establish regularity properties of the point-to-point free energy, and link it to the infinite volume point-to-line free energy and quenched large deviations of the walk. One corollary is a quenched large deviation principle for random walk in an ergodic random environment, with a continuous rate function.
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