Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 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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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: cond-mat