Random partitions and the Gamma kernel

Details Random partitions and the Gamma kernel Random partitions and the Gamma kernel

2003-05-21

arxiv.org/abs/math-ph/0305043v1

Adv. Math. 194 (2005), no. 1, 141--202

Physics

Mathematical Physics

AMSTeX, 49 pages

Scientific paper

We study the asymptotics of certain measures on partitions (the so-called z-measures and their relatives) in two different regimes: near the diagonal of the corresponding Young diagram and in the intermediate zone between the diagonal and the edge of the Young diagram. We prove that in both cases the limit correlation functions have determinantal form with a correlation kernel which depends on two real parameters. In the first case the correlation kernel is discrete, and it has a simple expression in terms of the gamma functions. In the second case the correlation kernel is continuous and translationally invariant, and it can be a written as a ratio of two suitably scaled hyperbolic sines.

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