Determinants of Laplacians on converging hyperbolic surfaces
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.
Fields of Study & Subjects
Geometry and complex manifolds
Mathematical Dynamics and Fractals
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 1 January 2026
- Document type
- Preprint