Brownian Loops and the Selberg Zeta Function
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _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 |