Asymptotics of q-plancherel measures

ASYMPTOTICS OF q-PLANCHEREL MEASURES

In this paper, we are interested in the asymptotic size of the rows and columns of a random Young diagram under a natural deformation of the Plancherel measure coming from Hecke algebras. The first lines of such diagrams are typically of order n, so it does not fit in the context of the work of P. Biane and P. Śniady. Using the theory of polynomial functions on Young diagrams of Kerov and Olsha...

Asymptotics of Plancherel Measures for Symmetric Groups

1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G∧ of irreducible representations of G which assigns to a representation π ∈ G∧ the weight (dim π)/|G|. For the symmetric group S(n), the set S(n)∧ is the set of partitions λ of the number n, which we shall identify with Young diagrams with n squares throughout th...

Asymptotics of Plancherel – Type Random Partitions

We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel–type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set Z+ of nonnegative integers. This can be viewed as an edge limit transition. The limit process is determined by a correlation kernel on Z+ which is expressed throug...

Jack Deformations of Plancherel Measures and Traceless Gaussian Random Matrices

We study random partitions λ = (λ1, λ2, . . . , λd) of n whose length is not bigger than a fixed number d. Suppose a random partition λ is distributed according to the Jack measure, which is a deformation of the Plancherel measure with a positive parameter α > 0. We prove that for all α > 0, in the limit as n → ∞, the joint distribution of scaled λ1, . . . , λd converges to the joint distributi...

Plancherel-Rotach asymptotics of second-order difference equations with linear coefficients