منابع مشابه
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...
متن کاملAsymptotics 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...
متن کاملJack 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...
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We consider a Markov evolution of lozenge tilings of a quarter-plane and study its asymptotics at large times. One of the boundary rays serves as a reflecting wall. We observe frozen and liquid regions, prove convergence of the local correlations to translation-invariant Gibbs measures in the liquid region, and obtain new discrete Jacobi and symmetric Pearcey determinantal point processes near ...
متن کامل• Fourier transform and Plancherel Theorem
When we try to transfer these three concepts to a “curved manifold” M , the situation becomes instantly very complicated. Let us look for an appropriate class of M ’s for which we can expect satisfactory answers. We need the requirement to measure distances, so M should be Riemannian. In order to have a reasonable theory of selfadjoint operators on M we also need completeness. But still the cla...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1992
ISSN: 0386-2194
DOI: 10.3792/pjaa.68.256