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 construct space-time stationary solutions of the $1 $ D Burgers equation with random
forcing in the absence of periodicity or any other compactness assumptions. More precisely …

We consider planar directed last-passage percolation on the square lattice with general iid
weights and study the geometry of the full set of semi-infinite geodesics in a typical …

We study the directed last-passage percolation model on the planar integer lattice with
nearest-neighbor steps and general iid weights on the vertices, outside the class of exactly …

The Kardar-Parisi-Zhang (KPZ) equation on the real line is well-known to admit Brownian
motion with a linear drift as a stationary distribution (modulo additive constants). We show …

In first-passage percolation, we place iid continuous weights at the edges of Z^ 2 Z 2 and
consider the weighted graph metric. A distance-minimizing path between points x and y is …

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 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 develop ergodic theory of the inviscid Burgers equation with random kick forcing in
noncompact setting. The results are parallel to those in our recent work on the Burgers …

We present a proof of the almost sure existence, uniqueness and coalescence of directed
semi-infinite geodesics in planar growth models that is based on properties of an increment …