Generalizations of some integrals over the unitary group

Abstract

Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and may also find applications in lattice gauge theory.

arXiv comment6 pages, some references added, version to appear in J. Phys. A: Special Issue on Random Matrix Theory

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Cited by in corpus (26)

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• Eigenvalue Density of Correlated Complex Random Wishart Matrices
• Exact Relation between Singular Value and Eigenvalue Statistics
• Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential
• On absolute moments of characteristic polynomials of a certain class of complex random matrices
• A few remarks on Colour-Flavour Transformations,truncations of random unitary matrices, Berezin reproducing kernels and Selberg type integrals
• Invariant Integration over the Unitary Group
• Statistical limits of dictionary learning: random matrix theory and the spectral replica method
• Mean field theory of effective spin models as a baryon fugacity expansion
• Rate of convergence of linear functions on the unitary group
• On matrix model partition functions for QCD with chemical potential
• On characteristic polynomials for a generalized chiral random matrix ensemble with a source
• Exact Large-Nc Solution of an Effective Theory for Polyakov Loops at Finite Chemical Potential
• Pizzetti formulae for Stiefel manifolds and applications
• Character expansion method for supergroups and extended superversions of the Leutwyler-Smilga and Berezin-Karpelevich integrals
• Finite Volume Gauge Theory Partition Functions in Three Dimensions
• Partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order
• The large N limit of SU(N) integrals in lattice models
• Level Repulsion in Constrained Gaussian Random-Matrix Ensembles
• Bosonic color-flavor transformation for the special unitary group
• Invariant and Group Theoretical Integrations over the U(n) Group
• Averages of products and ratios of characteristic polynomials in polynomial ensembles
• Grassmannian Integrals as Matrix Models for Non-Compact Yangian Invariants
• Grassmannian Integrals in Minkowski Signature, Amplitudes, and Integrability
• Generalised unitary group integrals of Ingham-Siegel and Fisher-Hartwig type
• A power series identity and Bessel-type integrals over unitary groups