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 …

The stationary horizon (SH) is a stochastic process of coupled Brownian motions indexed by
their real-valued drifts. It was first introduced by the first author as the diffusive scaling limit of …

Bi-infinite geodesics are fundamental objects of interest in planar first passage percolation.
A longstanding conjecture states that under mild conditions there are almost surely no …

Coalescence of semi-infinite geodesics remains a central question in planar first passage
percolation. In this paper, we study finer properties of the coalescence structure of finite and …

We establish fundamental properties of infinite geodesics and competition interfaces in the
directed landscape. We construct infinite geodesics in the directed landscape, establish their …

We study the last-passage growth model on the planar integer lattice with exponential
weights. With boundary conditions that represent the equilibrium exclusion process as seen …

In last passage percolation models lying in the KPZ universality class, long maximizing
paths have a typical deviation from the linear interpolation of their endpoints governed by …

The Directed Landscape, a random directed metric on the plane (where the first and the
second coordinates are termed spatial and temporal respectively), was constructed in the …

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 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 …