Matrix Correlators as Discrete Volumes of Moduli Space I: Recursion Relations, the BMN-limit and DSSYK

Alessandro Giacchetto; Pronobesh Maity; Edward A. Mazenc

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arXiv · 2510.17728

Matrix Correlators as Discrete Volumes of Moduli Space I: Recursion Relations, the BMN-limit and DSSYK

Alessandro Giacchetto·Pronobesh Maity·Edward A. Mazenc

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Abstract

We show certain correlators in generic one-matrix models define a notion of ``discrete'' volumes of the moduli space of Riemann surfaces, generalizing the connection between random matrices and JT gravity. We prove they obey a discrete, Mirzakhani-like recursion relation. Their fundamental discreteness crucially relies upon studying these matrix integrals away from the usual double-scaling limit. In a BMN-like limit of large traces, this recursion universally goes over to a continuous one, and the correlators asymptote to the volumes of Kontsevich. Finally, we demonstrate that the ETH matrix integral for DSSYK furnishes a discrete, $q$-analog of the Weil--Petersson volumes, thereby proving a conjecture due to K. Okuyama.

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Alessandro Giacchetto, Pronobesh Maity, Edward A. Mazenc. 2025-10-20. Matrix Correlators as Discrete Volumes of Moduli Space I: Recursion Relations, the BMN-limit and DSSYK. https://arxiv.org/abs/2510.17728

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