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Transportation of measure, Young diagrams and random matrices.

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Transportation of measure, Young diagrams and random matrices. / Blower, Gordon.

In: Bernoulli, Vol. 10, No. 5, 2004, p. 755-782.

Research output: Contribution to journalJournal articlepeer-review

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Blower, G 2004, 'Transportation of measure, Young diagrams and random matrices.', Bernoulli, vol. 10, no. 5, pp. 755-782.

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Blower, Gordon. / Transportation of measure, Young diagrams and random matrices. In: Bernoulli. 2004 ; Vol. 10, No. 5. pp. 755-782.

Bibtex

@article{7aa9c74fcf8249f9820d4b2defcb24b2,
title = "Transportation of measure, Young diagrams and random matrices.",
abstract = "The theory of transportation of mesure for general cost functions is used to obtain a novel logarithmic Sobolev inequality for measures on phase spaces of high dimension and hence a concentration of measure inequality. The are applications to Plancherel measure associated with the symmetric group, the distribution of Young diagrams partitioning N as N tends to infinity and to the mean field theory of random matrices. For the portential Gamma (N+1), the generalized orthogonal ensemble and its empirical eigenvalue distribution satisfy a Gaussian concentration of measure phenomenon. Hence the empirical eigenvalue distribution converges weakly almost surely as the matix size increases; the limiting density is given by the derivative of the Vershik probability density.",
keywords = "infinite symmetic group, logarithmic Sobolev inequality, Young tableaux",
author = "Gordon Blower",
year = "2004",
language = "English",
volume = "10",
pages = "755--782",
journal = "Bernoulli",
issn = "1350-7265",
publisher = "International Statistical Institute",
number = "5",

}

RIS

TY - JOUR

T1 - Transportation of measure, Young diagrams and random matrices.

AU - Blower, Gordon

PY - 2004

Y1 - 2004

N2 - The theory of transportation of mesure for general cost functions is used to obtain a novel logarithmic Sobolev inequality for measures on phase spaces of high dimension and hence a concentration of measure inequality. The are applications to Plancherel measure associated with the symmetric group, the distribution of Young diagrams partitioning N as N tends to infinity and to the mean field theory of random matrices. For the portential Gamma (N+1), the generalized orthogonal ensemble and its empirical eigenvalue distribution satisfy a Gaussian concentration of measure phenomenon. Hence the empirical eigenvalue distribution converges weakly almost surely as the matix size increases; the limiting density is given by the derivative of the Vershik probability density.

AB - The theory of transportation of mesure for general cost functions is used to obtain a novel logarithmic Sobolev inequality for measures on phase spaces of high dimension and hence a concentration of measure inequality. The are applications to Plancherel measure associated with the symmetric group, the distribution of Young diagrams partitioning N as N tends to infinity and to the mean field theory of random matrices. For the portential Gamma (N+1), the generalized orthogonal ensemble and its empirical eigenvalue distribution satisfy a Gaussian concentration of measure phenomenon. Hence the empirical eigenvalue distribution converges weakly almost surely as the matix size increases; the limiting density is given by the derivative of the Vershik probability density.

KW - infinite symmetic group

KW - logarithmic Sobolev inequality

KW - Young tableaux

M3 - Journal article

VL - 10

SP - 755

EP - 782

JO - Bernoulli

JF - Bernoulli

SN - 1350-7265

IS - 5

ER -