Research output: Contribution to journal › Journal article

Published

<mark>Journal publication date</mark> | 1/10/2001 |
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<mark>Journal</mark> | Journal of Statistical Physics |

Issue number | 1-2 |

Volume | 105 |

Number of pages | 27 |

Pages (from-to) | 309-335 |

<mark>State</mark> | Published |

<mark>Original language</mark> | English |

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.

RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics