We introduce a four-parameter family of interacting particle systems on the line, which can
be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which …

We consider a fully inhomogeneous stochastic higher spin six vertex model in a quadrant.
For this model we derive concise integral representations for multi-point q-moments of the …

We introduce an exactly-solvable model of random walk in random environment that we call
the Beta RWRE. This is a random walk in ZZ which performs nearest neighbour jumps with …

This paper is about a family of symmetric rational functions that form a one-parameter
generalization of the classical Hall–Littlewood polynomials. We introduce two sets of (skew …

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 …

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 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 prove that the $ q $-state Potts model and the random-cluster model with cluster weight
$ q> 4$ undergo a discontinuous phase transition on the square lattice. More precisely, we …

We revisit the problem of determining the Arctic curve in the six-vertex model with domain
wall boundary conditions. We describe an alternative method, by which we recover the …