Matrix models for circular ensembles

Details Matrix models for circular ensembles Matrix models for circular ensembles

2004-10-02

arxiv.org/abs/math/0410034v1

IMRN 50 (2004), 2665--2701

Mathematics

Spectral Theory

28 pages

Scientific paper

We describe an ensemble of (sparse) random matrices whose eigenvalues follow the Gibbs distribution for n particles of the Coulomb gas on the unit circle at inverse temperature beta. Our approach combines elements from the theory of orthogonal polynomials on the unit circle with ideas from recent work of Dumitriu and Edelman. In particular, we resolve a question left open by them: find a tri-diagonal model for the Jacobi ensemble.

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