Gaussian diagrammatics from circular ensembles of random matrices
Marcel Novaes · Journal of Physics A Mathematical and Theoretical · 2024
Abstract We uncover a hidden Gaussian ensemble inside each of the three circular ensembles of random matrices, providing novel diagrammatic rules for the calculation of moments. The matrices involved are generic complex for β = 2, complex symmetric for β = 1 and complex self-dual for β = 4, and at the last step their dimension must be set to 1 − 2 / β . As an application, we compute moments of traces of submatrices.