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Almost sure weak convergence for the circular ensembles of Dyson.

Blower, Gordon (2003) Almost sure weak convergence for the circular ensembles of Dyson. Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports, 75 (6). pp. 425-433. ISSN 1744-2508

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Abstract

The circular ensembles of Dyson satisfy isoperimetric inequalities and concentration of measure phenomena for large particle numbers analogous to the isoperimetric inequality for surface measure on the sphere in Euclidean space of high dimension. This leads to a geometrical proof of a result of Johansson [Bull. Sci. Math. (2) 112, (1988), 257-304] that the empirical distribution of energy levels under such ensembles converge weakly almost surely to normalized arclength on the unit circle as n→∞.

Item Type: Article
Journal or Publication Title: Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports
Uncontrolled Keywords: Random matrices ; Isoperimetric inequality ; Statistical mechanics ; Circular ensembles ; Primary ; 60K35 ; Secondary ; 47B06
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 9679
Deposited By: Mrs Yaling Zhang
Deposited On: 19 Jun 2008 14:53
Refereed?: Yes
Published?: Published
Last Modified: 08 Dec 2014 10:29
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/9679

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