Long Time Asymptotics of Heat Kernels and Brownian Winding Numbers on Manifolds with Boundary
نویسندگان
چکیده
Let M be a compact Riemannian manifold with smooth boundary. We obtain the exact long time asymptotic behaviour of heat kernel on abelian coverings mixed Dirichlet and Neumann boundary conditions. As an application, we study abelianized winding reflected Brownian motions in M. In particular, prove Gaussian type central limit theorem showing that when rescaled appropriately, fluctuations are normally distributed explicit covariance matrix.
منابع مشابه
Long Time Asymptotics of Heat Kernels and Brownian Winding Numbers on Manifolds with Boundary
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 ofM 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 t...
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ژورنال
عنوان ژورنال: ALEA-Latin American Journal of Probability and Mathematical Statistics
سال: 2021
ISSN: ['1980-0436']
DOI: https://doi.org/10.30757/alea.v18-48