Particle systems with repulsion exponent \(\beta\) and random matrices. (English) Zbl 1297.15040

Venker, Martin

Electron. Commun. Probab. 18, Paper No. 83, 12 p. (2013).

Summary: 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.

MSC:

15B52	Random matrices (algebraic aspects)
60B20	Random matrices (probabilistic aspects)
82C22	Interacting particle systems in time-dependent statistical mechanics

Keywords:

universality; \(\beta \)-ensembles; random matrices; repulsion