Multiple scale asymptotics of map enumeration

Author:

Ercolani NicholasORCID,Lega JocelineORCID,Tippings BrandonORCID

Abstract

Abstract We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar surfaces. Central to this work is the comparison of two asymptotic expansions obtained from two different fields of mathematics: the Riemann–Hilbert analysis of orthogonal polynomials and the theory of discrete dynamical systems. By equating the coefficients of these expansions in a common region of uniform validity in their parameters, we recover known results and provide new expressions for generating functions associated with graphical enumeration on surfaces of genera 0 through 7. Although the body of the article focuses on 4-valent maps, the methodology presented here extends to regular maps of arbitrary even valence and to some cases of odd valence, as detailed in the appendices.

Publisher

IOP Publishing

Subject

Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

Reference45 articles.

1. Matrix model calculations beyond the spherical limit;Ambjorn;Nucl. Phys. B,1993

2. Topological expansion in the cubic random matrix model;Bleher;Int. Math. Res. Not.,2013

3. Painlevé I double scaling limit in the cubic random matrix model;Bleher;Random Matrices: Theory Appl.,2016

4. Phase diagram and topological expansion in the complex quartic random matrix model;Bleher,2021

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