The first goal of this paper is to prove multiple asymptotic results for a time‐discrete and
space‐continuous polymer model of a random walk in a random potential. These results …

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 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 …

Random walk in a dynamic iid beta random environment, conditioned to escape at an
atypical velocity, converges to a Doob transform of the original walk. The Doob-transformed …

We present stochastic homogenization results for viscous Hamilton–Jacobi equations using
a new argument that is based only on the subadditive structure of maximal subsolutions (ie …

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 a bounded step size random walk in an ergodic random environment with
some ellipticity, on an integer lattice of arbitrary dimension. We prove a level 3 large …

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 …