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arXiv · 2409.17838

The factorial growth of topological recursion

Gaëtan Borot·Bertrand Eynard·Alessandro Giacchetto
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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 $g \rightarrow \infty$, 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.

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Gaëtan Borot, Bertrand Eynard, Alessandro Giacchetto. 2024-10-22. The factorial growth of topological recursion. https://doi.org/10.1007/s11005-025-01950-z

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