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 random walk in a space-time random potential, also known as directed random
polymer measures, on the planar square lattice with nearest-neighbor steps and general iid …

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 …

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 …

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 …

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 …

Consider a one-dimensional shift-invariant attractive spin-flip system in equilibrium,
constituting a dynamic random environment, together with a nearest-neighbor random walk …

We consider a one-dimensional simple symmetric exclusion process in equilibrium,
constituting a dynamic random environment for a nearest-neighbor random walk that on …

We prove a shape theorem and derive a variational formula for the limiting quenched
Lyapunov exponent and the Green's function of random walk in a random potential on a …