Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $\beta$

Gernot Akemann, Adam Mielke, Patricia Päßler

A random matrix representation is proposed for the two-dimensional (2D) Coulomb gas at inverse temperature $\beta$. For $2\times 2$ matrices with Gaussian distribution we analytically…