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:
Journal Article
Journal or Publication Title:
Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports
Uncontrolled Keywords:
/dk/atira/pure/researchoutput/libraryofcongress/qa
Subjects:
?? random matricesisoperimetric inequalitystatistical mechanicscircular ensemblesprimary60k35secondary47b06qa mathematics ??
ID Code:
9679
Deposited By:
Users 810 not found.
Deposited On:
19 Jun 2008 13:53
Refereed?:
Yes
Published?:
Published
Last Modified:
15 Jul 2024 11:42