Blower, Gordon (2001) *Almost sure weak convergence for the generalized orthogonal ensemble.* Journal of Statistical Physics, 105 (1-2). pp. 309-335. ISSN 0022-4715

## Abstract

The generalized orthogonal ensemble satisfies isoperimetric inequalities analogous to the Gaussian isoperimetric inequality, and an analogue of Wigner's law. Let v be a continuous and even real function such that V(X)=tracev(X)/n defines a uniformly p-convex function on the real symmetric n×n matrices X for some p2. Then (dX)=e –V(X) dX/Z satisfies deviation and transportation inequalities analogous to those satisfied by Gaussian measure(6, 27), but for the Schatten c p norm. The map, that associates to each XM s n () its ordered eigenvalue sequence, induces from a measure which satisfies similar inequalities. It follows from such concentration inequalities that the empirical distribution of eigenvalues converges weakly almost surely to some non-random compactly supported probability distribution as n.

Item Type: | Article |
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Journal or Publication Title: | Journal of Statistical Physics |

Additional Information: | RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics |

Uncontrolled Keywords: | random matrices - transportation - isoperimetric inequality - statistical mechanics |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 2367 |

Deposited By: | ep_importer |

Deposited On: | 01 Apr 2008 15:16 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 21 Sep 2017 03:25 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/2367 |

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