Brownian motion is a continuum scaling limit for a wide class of random processes, and
there has been great success in develo** a theory for its properties (such as distribution …

In a surprising sequence of developments, the longest increasing subsequence problem,
originally mentioned as merely a curious example in a 1961 paper, has proven to have deep …

Abstract We study a (1+ 1)-dimensional directed polymer in a random environment on the
integer lattice with log-gamma distributed weights. Among directed polymers, this model is …

We prove that the stationary measures for the free-energy increment process for the
geometric last passage percolation (LPP) and log-gamma polymer model on a diagonal …

We establish a fundamental connection between the geometric Robinson–Schensted–
Knuth (RSK) correspondence and GL (N, R)-Whittaker functions, analogous to the well …

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 …

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 …

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 …

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 …