Determinants of Laplacians on converging hyperbolic surfaces

Renan Gross; Guy Lachman; Asaf Nachmias

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arXiv · 2601.00338

Determinants of Laplacians on converging hyperbolic surfaces

Renan Gross·Guy Lachman·Asaf Nachmias

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Abstract

Let $S_k$ be a sequence of compact hyperbolic surfaces of increasing volume which locally converges to a random rooted surface. We show that if the normalized sum of the reciprocal lengths of very short simple closed geodesics converges to 0, then the normalized logarithm of the determinant of the Laplacian of $S_k$ converges to a constant depending only the law of the limiting surface.

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Renan Gross, Guy Lachman, Asaf Nachmias. 2026-01-01. Determinants of Laplacians on converging hyperbolic surfaces. https://arxiv.org/abs/2601.00338

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