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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: Article
    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
    ID Code: 1698
    Deposited By: Professor Gordon Blower
    Deposited On: 18 Feb 2008 09:35
    Refereed?: Yes
    Published?: Published
    Last Modified: 01 Apr 2016 01:04
    Identification Number:

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