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

## 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: | Article |
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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: | 26 Mar 2017 00:02 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/1698 |

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