P-2024-04
Gaëtan Borot, Bertrand Eynard, and Alessandro Giacchetto
The Factorial Growth of Topological Recursion
Abstract: We show that the n-point, genus-g correlation functions of topological recursion on
any regular spectral curve with simple ramifications grow at most like (2g − 2 + n)! as g → ∞,
which is the expected growth rate. This provides, in particular, an upper bound for many curve
counting problems in large genus and serves as a preliminary step for a resurgence analysis.
33 pp.
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2024-04