On the law of the index of Brownian loops related to the Hopf and anti-de Sitter fibrations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917801765109760 |
|---|---|
| author | Baudoin, Fabrice Kuijper, Teije |
| author_facet | Baudoin, Fabrice Kuijper, Teije |
| contents | We give explicit formulas and asymptotics for the distribution of the index of the Brownian loop in the following geometrical settings: the complex projective line from which two points have been removed; the complex hyperbolic line from which one point has been removed; the odd dimensional spheres from which a great hypersphere has been removed; and the complex anti-de Sitter spaces. Our analysis is based on the geometry of the Hopf and anti-de Sitter fibrations, and on the relationship between winding and area forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06824 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the law of the index of Brownian loops related to the Hopf and anti-de Sitter fibrations Baudoin, Fabrice Kuijper, Teije Probability Differential Geometry We give explicit formulas and asymptotics for the distribution of the index of the Brownian loop in the following geometrical settings: the complex projective line from which two points have been removed; the complex hyperbolic line from which one point has been removed; the odd dimensional spheres from which a great hypersphere has been removed; and the complex anti-de Sitter spaces. Our analysis is based on the geometry of the Hopf and anti-de Sitter fibrations, and on the relationship between winding and area forms. |
| title | On the law of the index of Brownian loops related to the Hopf and anti-de Sitter fibrations |
| topic | Probability Differential Geometry |
| url | https://arxiv.org/abs/2410.06824 |