Gaussian beta ensembles: the perfect freezing transition and its characterization in terms of Beurling-Landau densities

Yacin Ameur, Felipe Marceca, José Luis Romero

The Gaussian $\beta$-ensemble is a real $n$-point configuration $\{x_j{\}}_1^n$ picked randomly with respect to the Boltzmann factor $e^{-\frac{\beta }{2}{H}_n}$, $H_n=\sum_{i\ne j}\log\frac 1{|x_i…