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arXiv · 2510.12431

A q-analogue of Mirzakhani's recursion for Weil-Petersson volumes

Norman Do·Paul Norbury
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Abstract

We define q-analogues of Mirzakhani's recursion for Weil-Petersson volumes and the Stanford-Witten recursion for super Weil-Petersson volumes. Okuyama recently introduced a q-deformation of the Gaussian Hermitian matrix model which produces quasi-polynomials that recover the Weil-Petersson volumes via a rescaled q to 1 limit. The q-deformations of the Weil-Petersson volumes produced here agree with the top degree terms of Okuyama's quasi-polynomials and suggest a variation of Okuyama's methods to the super setting.

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Norman Do, Paul Norbury. 2025-10-14. A q-analogue of Mirzakhani's recursion for Weil-Petersson volumes. https://arxiv.org/abs/2510.12431

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