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Large Deviations Asymptotics for Spherical Integrals

โœ Scribed by Alice Guionnet; Ofer Zeitouni

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
554 KB
Volume
188
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

Consider the spherical integral

, where m b N denote the Haar measure on the orthogonal group O N when b=1 and on the unitary group U N when b=2, and D N , E N are diagonal real matrices whose spectral measures converge to m D , m E . In this paper we prove the existence and represent as solution to a variational problem the limit

N (D N , E N ). This limit appears in so-called ''matrix models'' but also in the evaluation of large deviations of the spectral measure of generalized Wishart matrices. Our technique is based on stochastic calculus, large deviations, and elements from free probability.

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