We solve the large deviations of the Kardar-Parisi-Zhang (KPZ) equation in one dimension
at short time by introducing an approach which combines field theoretical, probabilistic, and …

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

This work is dedicated to $\mathfrak {sl} _ {n+ 1} $-related integrable stochastic vertex
models; we call such models coloured. We prove several results about these models, which …

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 provide the first tight bounds on the lower tail probability of the one-point distribution of
the Kardar–Parisi–Zhang (KPZ) equation with narrow wedge initial data. Our bounds hold …

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 …

It was recently proved in Corwin and Shen (CPAM,[CS16]) that under weakly asymmetric
scaling, the height functions for ASEP with sources and sinks converges to the Hopf–Cole …

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 …

Fredholm determinants associated to deformations of the Airy kernel are closely connected
to the solution to the Kardar‐Parisi‐Zhang (KPZ) equation with narrow wedge initial data …

We consider the log-gamma polymer in the half-space with bulk weights distributed as
Gamma-1 (2 θ) and diagonal weights as Gamma-1 (α+ θ) for θ> 0 and α>-θ. We show that in …