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
Full text not available from this repository.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 |
|---|---|
| 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: | 26 Jul 2012 16:12 |
| Identification Number: | |
| URI: | http://eprints.lancs.ac.uk/id/eprint/2367 |
Actions (login required)
| View Item |
