PUB - Publikationen an der Universität Bielefeld

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 this yields a surmise for the nearest neighbour spacing distribution of complex eigenvalues in radial distance. It reproduces the 2D Poisson distribution at $\beta=0$ and approximates the complex Ginibre ensemble at $\beta=2$. The surmise is used to fit data from open quantum spin chains and ecology. The spacing distributions of complex symmetric and complex quaternion self-dual ensembles are fitted by non-integer values $\beta=1.4$ and $\beta=2.6$, respectively. They have been suggested as the only two symmetry classes with 2D bulk statistics different from the Ginibre ensemble.