Transportation of measure, Young diagrams and random matrices
type: Item
instance of: scholarly article
title: Transportation of measure, Young diagrams and random matrices
zbMATH Open document ID: 1065.60014
author: Gordon Blower
published in: Bernoulli
publication date: 2005-03-30T00:00:00Z
review text: The paper contains seven sections which present a new approach to transportation inequalities and the concentration-of-measure phenomenon for certain Gibbs measures on phase spaces of high dimension. In Section 2 basic results about tranportation of measure are given. In Section 4 the convexity properties of total energy are considered. Also logarithmic Sobolev inequalities and concentration inequalities for the continuous Gibbs measure are deduced. These results are deduced from an abstract logarithmic Sobolev inequality for general convex cost functions that is presented in Section 3. In Section 5 the empirical distribution of row lengths of Young diagrams is considered. In Section 6 it is shown how a special probability measure does indeed arise for the joint eigenvalue distributions of Dyson's generalized orthogonal ensemble with potential function \(\log\Gamma(1+x)\). Using the concentration inequalities of Section 6, in Section 7 convergence properties for various correlation functions associated with the random matrices are obtained.
reviewed by: U. A. Rozikov
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 82B44
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 60C05
zbMATH DE Number: 2149080
zbMATH Keywords: infinite symmetric group
zbMATH Keywords: logarithmic Sobolev inequality
zbMATH Keywords: Young tableau
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3150/bj/1099579155
OpenAlex ID: W2037225783
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DOI: 10.3150/BJ/1099579155
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description: scientific article; zbMATH DE number 2149080