The Harer--Zagier recursion for an irregular spectral curve

Abstract

We derive the Do and Norbury recursion formula for the one-loop mean of an irregular spectral curve from a variant of replica method by Brezín and Hikami. We express this recursion in special times in which all terms $W_1^{(g)}$ of the genus expansion of the one-loop mean are polynomials. We find a generalization of this recursion to the generalized Laguerre polynomial case.

16 pages, no figures, presentation reshuffled, typos corrected, examples added

References in corpus (8)

• On KP-integrable Hurwitz functions
• Intersection theory from duality and replica
• The matrix model for hypergeometric Hurwitz numbers
• Matrix models and a proof of the open analog of Witten's conjecture
• From Brezin-Hikami to Harer-Zagier formulas for Gaussian correlators
• Topological recursion for irregular spectral curves
• Open intersection numbers, matrix models and MKP hierarchy
• Models of discretized moduli spaces, cohomological field theories, and Gaussian means

Cited by in corpus (2)

• On Products of Random Matrices
• Topological recursion on the Bessel curve