Particle Systems with Repulsion Exponent $\beta$ and Random Matrices

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.

12 pages; has been rewritten as a note

References in corpus (4)

• First order global asymptotics for confined particles with singular pair repulsion
• Fluctuations of eigenvalues of matrix models and their applications
• Bulk Universality of General $\beta$-Ensembles with Non-convex Potential
• Local universality of repulsive particle systems and random matrices

Cited by in corpus (3)

• The high temperature crossover for general 2D Coulomb gases
• Local universality of repulsive particle systems and random matrices
• Interactions Between Different Birds of Prey as a Random Point Process