This note is an expanded version of a lecture I gave in fall 2021 at the MSRI program
“Universality and Integrability in Random Matrices and Interacting Particle Systems”. I will …

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 review recent progress on the study of the Kardar–Parisi–Zhang (KPZ) equation in a
periodic setting, which describes the random growth of an interface in a cylindrical geometry …

We obtain a simple formula for the stationary measure of the height field evolving according
to the Kardar-Parisi-Zhang equation on the interval $[0, L] $ with general Neumann type …

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 introduce a family of multi-dimensional Askey–Wilson signed measures. We offer an
explicit description of the stationary measure of the open asymmetric simple exclusion …

This paper builds upon the research of Corwin and Knizel who proved the existence of
stationary measures for the KPZ equation on an interval and characterized them through a …

We present an exact solution for the height distribution of the KPZ equation at any time t in a
half space with flat initial condition. This is equivalent to obtaining the free-energy …

Abstract We study the Kardar–Parisi–Zhang (KPZ) equation on the half-line x⩾ 0 with
Neumann type boundary condition. Stationary measures of the KPZ dynamics were …

The stationary measures of the Kardar–Parisi–Zhang equation on an interval have been
computed recently. We present a rather direct derivation of this result by taking the weak …