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2013 Particle systems with repulsion exponent $\beta$ and random matrices
Martin Venker
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Electron. Commun. Probab. 18: 1-12 (2013). DOI: 10.1214/ECP.v18-2864

Abstract

We consider a class of particle systems generalizing the $\beta$ Ensembles from random matrix theory. In these new ensembles, particles experience repulsion of power $\beta>0$ when getting close, which is the same as in the $\beta$-Ensembles. For distances larger than zero, the interaction is allowed to differ from those present for random eigenvalues. We show that the local bulk correlations of the $\beta$-Ensembles, universal in random matrix theory, also appear in these new ensembles.

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Martin Venker. "Particle systems with repulsion exponent $\beta$ and random matrices." Electron. Commun. Probab. 18 1 - 12, 2013. https://doi.org/10.1214/ECP.v18-2864

Information

Accepted: 3 November 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1297.15040
MathSciNet: MR3141792
Digital Object Identifier: 10.1214/ECP.v18-2864

Subjects:
Primary: 15B52
Secondary: 60B20, 82C22

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