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 …

We explore probabilistic consequences of correspondences between $ q $-Whittaker
measures and periodic and free boundary Schur measures established by the authors in the …

We consider the asymmetric simple exclusion process (ASEP) on the positive integers with
an open boundary condition. We show that, when starting devoid of particles and for a …

We consider ASEP on a bounded interval and on a half‐line with sources and sinks. On the
full line, Bertini and Giacomin in 1997 proved convergence under weakly asymmetric …

We construct explicit one-parameter families of stationary measures for the Kardar–Parisi–
Zhang equation in half-space with Neumann boundary conditions at the origin, as well as for …

We develop a new probabilistic and geometric method to obtain several sharp results
pertaining to the upper tail behavior for the Kardar-Parisi-Zhang (KPZ) equation in a unified …

These are lecture notes for a mini-course given at the Cornell Probability Summer School in
July 2013. Topics include lozenge tilings of polygons and their representation theoretic …

We consider the point-to-point log-gamma polymer of length 2 N in a half-space with iid
Gamma-1 (2 θ) distributed bulk weights and iid Gamma-1 (α+ θ) distributed boundary …

We survey recent work within the area of algebraic combinatorics that has the flavor of
discrete dynamical systems, with a particular focus on the homomesy phenomenon codified …