Matrix models for circular ensembles

R. Killip; I. Nenciu

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arXiv · math/0410034

Matrix models for circular ensembles

R. Killip·I. Nenciu

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Abstract

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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BibTeX RIS

R. Killip, I. Nenciu. 2004-10-02. Matrix models for circular ensembles. https://arxiv.org/abs/math/0410034

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