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Displacement convexity for the generalized orthogonal ensemble.

Research output: Contribution to journalJournal article

Published

Journal publication date09/2004
JournalJournal of Statistical Physics
Journal number5/6
Volume116
Number of pages29
Pages1359-1387
Original languageEnglish

Abstract

The paper considers the generalized ensemble of n by n real symmetric matrices that is invariant under the natural action of the real orthogonal group and that is given by a real potential function. Under various conditions on the potential, the empirical eigenvalue distributions converge weakly almost surely to a non random equilibrium measure as n tends to infinity. The logarithmic energy is displacement convex as a functional on charge distributions with fixed mean on the real line for such potentials.

Bibliographic note

The original publication is available at www.springerlink.com