Long Time Asymptotics of Heat Kernels and Brownian Winding Numbers on Manifolds with Boundary
| Autor: | Gautam Iyer, Xi Geng |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Probability (math.PR) 010102 general mathematics Mathematical analysis Boundary (topology) Riemannian manifold Type (model theory) 01 natural sciences 010104 statistics & probability Mathematics - Analysis of PDEs FOS: Mathematics Neumann boundary condition 0101 mathematics Abelian group Mathematics - Probability Heat kernel Brownian motion Analysis of PDEs (math.AP) Mathematics Central limit theorem |
| Zdroj: | Latin American Journal of Probability and Mathematical Statistics. 18:1297 |
| ISSN: | 1980-0436 |
| DOI: | 10.30757/alea.v18-48 |
| Popis: | Let M be a compact Riemannian manifold with smooth boundary. We obtain the exact long time asymptotic behaviour of the heat kernel on abelian coverings of M with mixed Dirichlet and Neumann boundary conditions. As an application, we study the long time behaviour of the abelianized winding of reflected Brownian motions in M. In particular, we prove a Gaussian type central limit theorem showing that when rescaled appropriately, the fluctuations of the abelianized winding are normally distributed with an explicit covariance matrix. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|