Determinants of Laplacians on random hyperbolic surfaces
Spectral Theory
2023-12-19 v4 Differential Geometry
Abstract
We investigate the behaviour of the regularized determinant of the Laplace-Beltrami operator on compact hyperbolic surfaces when the genus goes to infinity. We show that for all popular models of random surfaces, with high probability as the genus goes to infinity, the determinant has an exponential growth with a universal exponent. Limit results for some moments of the logarithm of the determinant are then derived.
Keywords
Cite
@article{arxiv.2301.09965,
title = {Determinants of Laplacians on random hyperbolic surfaces},
author = {Frédéric Naud},
journal= {arXiv preprint arXiv:2301.09965},
year = {2023}
}
Comments
20 pages, revised version