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 $g\to \infty$, 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.

33 pages. Comments are welcome! v2: added references

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Cited by in corpus (1)

• Quantum Curve for strip geometries, Topological Recursion and open GW/DT invariants