Topological Expansion of Oscillatory BGW and HCIZ Integrals at Strong Coupling

2022/03/21 by Jonathan Novak, Novak, Jonathan · 1 citation
Mathematics · Biochemistry, Genetics and Molecular Biology · #Mathematical Dynamics and Fractals #Caveolin-1 and cellular processes

paper · pdf · doi:10.48550/arxiv.2203.10746

Abstract

We prove that the BGW and HCIZ integrals admit large N topological expansions for complex coupling and complex external fields, provided the coupling is sufficiently strong. The expansion coefficients are holomorphic functions which are genus-specific generating functions for the monotone single and double Hurwitz numbers, respectively.

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• Jacobi polynomials on the simplex of Hermitian matrices and zonal spherical functions on partial flag manifolds

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