Vadim Gorin

Stochastic six-vertex model

We study the asymmetric six-vertex model in the quadrant with parameters on the stochastic line. We show that the random height function of the model converges to an explicit deterministic limit shape as the mesh size tends to 0. We further prove that the one-point fluctuations around the limit shape are asymptotically governed by the GUE Tracy-Widom distribution. We also explain an equivalent formulation of our model as an interacting particle system, which can be viewed as a discrete time generalization of ASEP started from the step initial condition. Our results confirm an earlier prediction of Gwa and Spohn (1992) that this system belongs to the KPZ universality class.

Nonintersecting paths and the Hahn orthogonal polynomial ensemble

We compute the bulk limit of the correlation functions for the uniform measure on lozenge tilings of a hexagon. The limiting determinantal process is a translation-invariant extension of the discrete sine process, which can also be described by an ergodic Gibbs measure with appropriate parameters.

Asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory

We develop a new method for studying the asymptotics of symmetric polynomials of representation- theoretic origin as the number of variables tends to infinity. Several applications of our method are presented: We prove a number of theorems concerning characters of infinite-dimensional unitary group and their q-deformations. We study the behavior of uniformly random lozenge tilings of large polygonal domains and find the GUE-eigenvalues distribution in the limit. We also investigate similar behavior for Alternating Sign Matrices (equivalently, six-vertex model with domain wall boundary conditions). Finally, we compute the asymptotic expansion of certain observables in theO(n = 1) dense loop model.

Fluctuations of particle systems determined by Schur generating functions

Abstract We develop a new toolbox for the analysis of the global behavior of stochastic discrete particle systems. We introduce and study the notion of the Schur generating function of a random discrete configuration. Our main result provides a Central Limit Theorem (CLT) for such a configuration given certain conditions on the Schur generating function. As applications of this approach, we prove CLTs for several probabilistic models coming from asymptotic representation theory and statistical physics, including random lozenge and domino tilings, non-intersecting random walks, decompositions of tensor products of representations of unitary groups.

Limits of multilevel TASEP and similar processes

We study the asymptotic behavior of a class of stochastic dynamics on interlacing particle configurations (also known as Gelfand-Tsetlin patterns). Examples of such dynamics include, in particular, a multi-layer extension of TASEP and particle dynamics related to the shuffling algorithm for domino tilings of the Aztec diamond. We prove that the process of reflected interlacing Brownian motions introduced by Warren in \cite{W} serves as a universal scaling limit for such dynamics.

Gaussian asymptotics of discrete

We introduce and study stochastic N

\beta

N

-ensembles

-particle ensembles which are discretizations for general-β

From Alternating Sign Matrices to the Gaussian Unitary Ensemble

\beta

Estimation of Multivariate Observation-Error Statistics for AMSU-A Data

log-gases of random matrix theory. The examples include random tilings, families of non-intersecting paths, (z,w)