Blower, Gordon (2004) Transportation of measure, Young diagrams and random matrices. Bernoulli, 10 (5). pp. 755-782. ISSN 1350-7265Full text not available from this repository.
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.
|Journal or Publication Title:||Bernoulli|
|Uncontrolled Keywords:||infinite symmetic group ; logarithmic Sobolev inequality ; Young tableaux|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Mathematics and Statistics|
|Deposited By:||Professor Gordon Blower|
|Deposited On:||18 Feb 2008 09:35|
|Last Modified:||03 Dec 2016 01:15|
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