5 papers
Macroscopic asymptotics in discrete beta-ensembles and random tilings
Gaëtan Borot, Vadim Gorin, Alice Guionnet
We carry out the asymptotic analysis of repulsive ensembles of N particles which are discrete analogues of continuous 1d log-gases or beta-ensembles of random matrix theory. The en…
On the Martin boundary for discrete TASEP
Vadim Gorin, Sergei Korotkikh
We study a problem with three equivalent formulations: describing Gibbs measures for five-vertex model in quadrant; classifying coherent systems on a p-deformation of the Gelfand-T…
Eigenvalues of Heckman-Polychronakos operators
Charles Dunkl, Vadim Gorin
Heckman-Polychronakos operators form a prominent family of commuting differential-difference operators defined in terms of the Dunkl operators as $\mathcal P_m= \sum…
Airy line ensemble and its Laplace transform
Vadim Gorin, Jiaming Xu, Lingfu Zhang
The Airy line ensemble is a random collection of continuous curves, which should serve as a universal edge scaling limit in problems related to eigenvalues of random matrices a…
Six-vertex model with rare corners and random restricted permutations
Vadim Gorin, Richard Kenyon
We study limit shapes in two equivalent models: the six-vertex model in the limit and the random Mallows permutation with restricted permutation matrix. We give the Euler-L…