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arXiv · 1804.00368

Long Time Asymptotics of Heat Kernels and Brownian Winding Numbers on Manifolds with Boundary

Xi Geng·Gautam Iyer
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Abstract

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.

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Xi Geng, Gautam Iyer. 2018-04-02. Long Time Asymptotics of Heat Kernels and Brownian Winding Numbers on Manifolds with Boundary. https://arxiv.org/abs/1804.00368

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