These are lecture notes for a mini-course given at the St. Petersburg School in Probability
and Statistical Physics in June 2012. Topics include integrable models of random growth …

A Gelfand–Tsetlin scheme of depth NN is a triangular array with mm integers at level mm,
m= 1, ..., N m= 1,…, N, subject to certain interlacing constraints. We study the ensemble of …

In this paper we consider uniformly random lozenge tilings of arbitrary domains
approximating (after suitable normalization) a closed, simply-connected subset of $\mathbb …

We investigate the free boundary Schur process, a variant of the Schur process introduced
by Okounkov and Reshetikhin, where we allow the first and the last partitions to be arbitrary …

We study the correlation functions for determinantal point processes defined by products of
infinite minors of block Toeplitz matrices. The motivation for studying such processes comes …

We construct discrete time Markov chains that preserve the class of Schur processes on
partitions and signatures. One application is a simple exact sampling algorithm for …

We introduce a general model of dimer coverings of certain plane bipartite graphs, which we
call rail yard graphs (RYG). The transfer matrices used to compute the partition function are …

We study a one-parameter family of probability measures on lozenge tilings of large regular
hexagons that interpolates between the uniform measure on all possible tilings and a …

We study Markov chains formed by squared singular values of products of truncated
orthogonal, unitary, symplectic matrices (corresponding to the Dyson index β= 1, 2, 4 …

We use the periodic Schur process, introduced in (Borodin in Duke Math J 140 (3): 391–468
2007), to study the random height function of lozenge tilings (equivalently, dimers) on an …