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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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
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 1698
Deposited By: Professor Gordon Blower
Deposited On: 18 Feb 2008 09:35
Refereed?: Yes
Published?: Published
Last Modified: 22 Feb 2020 01:17

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