The conjectured limit of last passage percolation is a scale-invariant, independent,
stationary increment process with respect to metric composition. We prove this for Brownian …

We provide a framework for proving convergence to the directed landscape, the central
object in the Kardar-Parisi-Zhang universality class. For last passage models, we show that …

We show that geodesics in the directed landscape have 3/2-variation and that weight
functions along the geodesics have cubic variation. We show that the geodesic and its …

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 …

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 …

We consider directed last passage percolation on Z^ 2 Z 2 with exponential passage times
on the vertices. A topic of great interest is the coupling structure of the weights of geodesics …

In 2002, Johansson conjectured that the maximum of the Airy 2 process minus the parabola
x 2 is almost surely achieved at a unique location [Joh03, Conjecture 1.5]. This result was …

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 …

We investigate the stationary distribution of asymmetric and weakly asymmetric simple
exclusion processes with open boundaries. We project the stationary distribution onto a …

This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite
geodesics in directed planar last-passage percolation with exponential weights. The …