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Hauptverfasser:	Lemonde, Roman, Wang, Jian
Format:	Preprint
Veröffentlicht:	2026
Schlagworte:	Probability Geometric Topology Spectral Theory
Online-Zugang:	https://arxiv.org/abs/2601.13086
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

_version_	1866917210322108416
author	Lemonde, Roman Wang, Jian
author_facet	Lemonde, Roman Wang, Jian
contents	We study the Brownian loop measure on hyperbolic surfaces for Brownian motion with a constant killing rate. We compute the mass of Brownian loops with killing in a free homotopy class and then relate the total mass of loops in all essential homotopy classes to the Selberg zeta function when the surface is geometrically finite. As an application, we provide a probabilistic interpretation of different notions of regularized determinants of Laplacian, in both the compact and infinite-area cases.
format	Preprint
id	arxiv_https___arxiv_org_abs_2601_13086
institution	arXiv
publishDate	2026
record_format	arxiv
spellingShingle	Brownian Loops and the Selberg Zeta Function Lemonde, Roman Wang, Jian Probability Geometric Topology Spectral Theory We study the Brownian loop measure on hyperbolic surfaces for Brownian motion with a constant killing rate. We compute the mass of Brownian loops with killing in a free homotopy class and then relate the total mass of loops in all essential homotopy classes to the Selberg zeta function when the surface is geometrically finite. As an application, we provide a probabilistic interpretation of different notions of regularized determinants of Laplacian, in both the compact and infinite-area cases.
title	Brownian Loops and the Selberg Zeta Function
topic	Probability Geometric Topology Spectral Theory
url	https://arxiv.org/abs/2601.13086

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