First-passage percolation (FPP) is a fundamental model in probability theory that has a wide
range of applications to other scientific areas (growth and infection in biology, optimization in …

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

We study first-passage percolation on Z^ 2 Z 2, where the edge weights are given by a
translation-ergodic distribution, addressing questions related to existence and coalescence …

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 …

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 prove that the variance of the passage time from the origin to a point xx in first-passage
percolation on Z^ d Z d is sublinear in the distance to xx when d ≥ 2 d≥ 2, obeying the …

We study Busemann functions, semi-infinite geodesics, and competition interfaces in the
exactly solvable last-passage percolation with inhomogeneous exponential weights. New …

For directed polymers, the shape function computes the limiting average energy accrued by
paths with a given average slope. We prove that, for a large family of directed polymer …

First passage percolation on Z^ 2 Z 2 is a model for describing the spread of an infection on
the sites of the square lattice. The infection is spread via nearest neighbor sites and the time …

We discuss the order of the variance on a lattice analogue of the Hammersley process with
boundaries, for which the environment on each site has independent, Bernoulli distributed …