1209.3178 (Martin Venker)

Particle Systems with Repulsion Exponent β and Random Matrices    [PDF]

Martin Venker

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. This result extends the bulk universality classes of random matrix theory and may lead to a better understanding of the occurrences of random matrix bulk statistics in several observations which have no obvious connection to random matrices. The present work is a generalization of [GV12] where a similar result was proved for \beta=2.

View original: http://arxiv.org/abs/1209.3178