1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set Gâˆ§ of irreducible representations of G which assigns to aâ€¦ (More)

Abstract. One object of interest in random matrix theory is a family of point ensembles (random point configurations) related to various systems of classical orthogonal polynomials. The paper dealsâ€¦ (More)

We introduce and study a 2â€“parameter family of unitarily invariant probability measures on the space of infinite Hermitian matrices. We show that the decomposition of a measure from this family onâ€¦ (More)

We construct a family of stochastic growth models in 2+1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1 + 1 dimensional growth models in the KPZâ€¦ (More)

Our interest is in the cumulative probabilities Pr(L(t) l) for the maximum length of increasing subsequences in Poissonized ensembles of random permutations, random fixed point free involutions andâ€¦ (More)

We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaf-fian/determinantal formulasâ€¦ (More)

We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants with a kernelâ€¦ (More)

We give simple linear algebraic proofs of Eynard-Mehta theorem, Okoun-kov-Reshetikhin formula for the correlation kernel of the Schur process, and Pfaffian analogs of these results. We also discussâ€¦ (More)

We consider two models for directed polymers in space-time independent random media (the Oâ€™Connell-Yor semi-discrete directed polymer and the continuum directed random polymer) at positiveâ€¦ (More)

We study certain probability measures on partitions of n = 1, 2, . . . , originated in representation theory, and demonstrate their connections with random matrix theory and multivariateâ€¦ (More)