A new approach to derive Pfaffian structures for random matrix ensembles

Abstract

Correlation functions for matrix ensembles with orthogonal and unitarysymplectic rotation symmetry are more complicated to calculate than in the unitary case. The supersymmetry method and the orthogonal polynomials are two techniques to tackle this task. Recently, we presented a new method to average ratios of characteristic polynomials over matrix ensembles invariant under the unitary group. Here, we extend this approach to ensembles with orthogonal and unitary-symplectic rotation symmetry. We show that Pfaffian structures can be derived for a wide class of orthogonal and unitary-symplectic rotation invariant ensembles in a unifying way. This includes also those for which this structure was not known previously, as the real Ginibre ensemble and the Gaussian real chiral ensemble with two independent matrices as well.

17 pages; 2 tables

References in corpus (11)

• Derivation of determinantal structures for random matrix ensembles in a new way
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• Comparison of the superbosonization formula and the generalized Hubbard-Stratonovich transformation
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• Random matrix ensembles involving Gaussian Wigner and Wishart matrices, and biorthogonal structure
• Completing the picture for the smallest eigenvalue of real Wishart matrices
• On Random Matrix Averages Involving Half-Integer Powers of GOE Characteristic Polynomials
• GUE-chGUE Transition preserving Chirality at finite Matrix Size
• Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices
• On the Efetov-Wegner terms by diagonalizing a Hermitian supermatrix
• Winding Number Statistics for Chiral Random Matrices: Averaging Ratios of Determinants with Parametric Dependence
• Winding Number Statistics for Chiral Random Matrices: Averaging Ratios of Parametric Determinants in the Orthogonal Case
• Asymptotic Coincidence of the Statistics for Degenerate and Non-Degenerate Correlated Real Wishart Ensembles
• Complex symmetric, self-dual, and Ginibre random matrices: Analytical results for three classes of bulk and edge statistics
• Statistical Topology -- Distribution and Density Correlations of Winding Numbers in Chiral Systems
• Fox H-kernel and $\theta$-deformation of the Cauchy two-matrix model and Bures ensemble
• Winding Number Statistics for Chiral Random Matrices: Universal Correlations and Statistical Moments in the Unitary Case