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 …

We discuss variational formulas for the law of large numbers limits of certain models of
motion in a random medium: namely, the limiting time constant for last-passage percolation …

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 …

Random walk in random environment (RWRE) is a fundamental model of statistical
mechanics, describing the movement of a particle in a highly disordered and …

We give two variational formulas (qVar1) and (qVar2) for the quenched free energy of a
random walk in random potential (RWRP) when (i) the underlying walk is directed or …

In 2003, Varadhan (Comm. Pure Appl. Math. 56 (2003) 1222–1245) developed a robust
method for proving quenched and averaged large deviations for random walks in a …

We consider the quenched and the averaged (or annealed) large deviation rate functions I q
and I a for space-time and (the usual) space-only RWRE on Z^ d. By Jensen's inequality, I …

We consider random walks in random Dirichlet environment (RWDE) which is a special type
of random walks in random environment where the exit probabilities at each site are iid …

In this work, we establish the existence of large deviation principles of random walk in
strongly mixing environments. The quenched and annealed rate functions have the same …

We establish the existence of generalized Busemann functions and Gibbs-Dobrushin-
Landford-Ruelle measures for a general class of lattice random walks in random potential …