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

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