Gaussian beta ensembles : The perfect freezing transition and its characterization in terms of Beurling–Landau densities
The Gaussian β-ensemble is a real n-point configuration {xj}n1 picked randomly with respect to the Boltzmann factor e− β 2 Hn, where Hn = ∑i≠j log |xi−1xj| + n ∑ni=112 xi2. It is well known that the point process {xj }n1 tends to follow the semicircle law σ (x) = 21π√(4 − x2 )+ in certain average senses. A Fekete configuration (minimizer of Hn) is spread out in a much more uniform way in the inter
