Large genus asymptotics for frequency of non-simple curves

Mingkun Liu; Kasra Rafi; Juan Souto; Marie Trin

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arXiv · 2605.03833

Large genus asymptotics for frequency of non-simple curves

Mingkun Liu·Kasra Rafi·Juan Souto·Marie Trin

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Abstract

We give an expression for the frequency of non-simple curves in closed surfaces and exploit it to study relative frequencies of such curves in large genus. This extend to the case of non-simple curves Mirzakhani's expressions of frequencies in terms of Konsevitch polynomials and Delecroix-Goujard-Zograf-Zorich large genus asymptotics for those frequencies. In particular, with K fixed, we identify which types of curves with K intersections are most common.

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Mingkun Liu, Kasra Rafi, Juan Souto, Marie Trin. 2026-05-05. Large genus asymptotics for frequency of non-simple curves. https://arxiv.org/abs/2605.03833

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