## Abstract

For sequences (*X*_{j}) of random closed hyperbolic surfaces with volume Vol(*X*_{j}) tending to infinity, we prove that there exists a universal constant *E* > 0 such that for all *ϵ* > 0, the regularized determinant of the Laplacian satisfies

with high probability as *j* → +⋡. This result holds for various models of random surfaces, including the Weil–Petersson model.

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## Acknowledgement

It is a pleasure to thank my neighbor Bram Petri for several discussions around this work. Thanks to Yuhao Xue and an anonymous referee for pointing out an improvement of Theorem 3.1. I also thank ZeevRudnick for his reading and comments. Finally, Yunhui Wu and Yuxin He have recently shown to me that Theorem 5.1 can also be refined in the Weil–Petterson case; see in §5 for details.

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*Dedicated to Peter Sarnak on the occasion of his 70th birthday*

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Naud, F. Determinants of Laplacians on random hyperbolic surfaces.
*JAMA* **151**, 265–291 (2023). https://doi.org/10.1007/s11854-023-0334-8

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DOI: https://doi.org/10.1007/s11854-023-0334-8