Gaussian diagrammatics from Circular Ensembles of random matrices
Abstract
We uncover a hidden Gaussian ensemble inside each of the three circular ensembles of random matrices, which provide 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 their dimension must be set to 1-2/β. As an application, we compute moments of traces of submatrices.
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