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