On the proof of Universality for orthogonal and symplectic ensembles in random matrix theory

Ovidiu Costin, Percy Deift, Dimitri Gioev

Research output: Contribution to journalArticle

Abstract

We give a streamlined proof of a quantitative version of a result from P. Deift and D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles. IMRP Int. Math. Res. Pap. (in press) which is crucial for the proof of universality in the bulk P. Deift and D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles. IMRP Int. Math. Res. Pap. (in press) and also at the edge P. Deift and D. Gioev, {Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices. Comm. Pure Appl. Math. (in press) for orthogonal and symplectic ensembles of random matrices. As a byproduct, this result gives asymptotic information on a certain ratio of the β=1,2,4 partition functions for log gases.

Original languageEnglish (US)
Pages (from-to)937-948
Number of pages12
JournalJournal of Statistical Physics
Volume129
Issue number5-6
DOIs
StatePublished - Oct 1 2007

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Keywords

  • Log gases
  • Orthogonal and symplectic ensembles
  • Partition function
  • Random matrix theory
  • Universality

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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