Almost sure weak convergence for the generalized orthogonal ensemble.

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

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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.

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Journal Article
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Journal of Statistical Physics
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RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics
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01 Apr 2008 14:16
Last Modified:
21 Nov 2022 19:12