Universality of General $β$-Ensembles

Paul Bourgade, Laszlo Erdos, Horng-Tzer Yau

Published 2011-04-12, updated 2012-02-05Version 5

We prove the universality of the $\beta$-ensembles with convex analytic potentials and for any $\beta>0$, i.e. we show that the spacing distributions of log-gases at any inverse temperature $\beta$ coincide with those of the Gaussian $\beta$-ensembles.