The Harer--Zagier recursion for an irregular spectral curve
Mathematical Physics
2016-11-21 v2 High Energy Physics - Theory
Geometric Topology
math.MP
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 Brez\'in and Hikami. We express this recursion in special times in which all terms of the genus expansion of the one-loop mean are polynomials. We find a generalization of this recursion to the generalized Laguerre polynomial case.
Keywords
Cite
@article{arxiv.1512.09278,
title = {The Harer--Zagier recursion for an irregular spectral curve},
author = {Leonid O. Chekhov},
journal= {arXiv preprint arXiv:1512.09278},
year = {2016}
}
Comments
16 pages, no figures, presentation reshuffled, typos corrected, examples added