Gamma-function singularity conjecture for beta-ensemble free energies
Let Vd+1(x)V_{d+1}(x)Vd+1(x) be any potential of degree d+1d+1d+1, and let ϵ~i{\widetilde{\epsilon}}_iϵi be the occupation numbers on the cycles A~i{\widetilde{{\cal A}}}_iAi, for i=1,…,di=1,\ldots,di=1,…,d. Here…