Transportation of measure, Young diagrams and random matrices.

Blower, Gordon (2004) Transportation of measure, Young diagrams and random matrices. Bernoulli, 10 (5). pp. 755-782. ISSN 1350-7265

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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.

Item Type:
Journal Article
Journal or Publication Title:
Bernoulli
Uncontrolled Keywords:
/dk/atira/pure/researchoutput/libraryofcongress/qa
Subjects:
ID Code:
1698
Deposited By:
Deposited On:
18 Feb 2008 09:35
Refereed?:
Yes
Published?:
Published
Last Modified:
27 Sep 2020 23:55