Quenched point-to-point free energy for random walks in random potentials |
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Authors: | Firas Rassoul-Agha Timo Seppäläinen |
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Institution: | 1. Mathematics Department, University of Utah, 155 South 1400 East, Salt Lake City, UT, 84109, USA 2. Mathematics Department, University of Wisconsin-Madison, 419 Van Vleck Hall, Madison, WI, 53706, USA
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Abstract: | 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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