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arXiv · 2610.16818

Very high genus double Hurwitz numbers via mixing times

Baptiste Louf·Lucas Teyssier
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Abstract

We obtain very high genus asymptotics for double Hurwitz numbers when both the size $n$ and the genus $g$ go to infinity, under the constraint that $g$ grows much faster than $n$, more precisely that $\frac{2g}{n}-\ln n\to\infty$. Our proof relies on adapting arguments about the mixing time of the transposition random walk introduced by Diaconis and Shahshahani.

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Baptiste Louf, Lucas Teyssier. 2026-10-12. Very high genus double Hurwitz numbers via mixing times. https://arxiv.org/abs/2610.16818

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