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# Gautam Iyer : Winding of Brownian trajectories and heat kernels on covering spaces

## root

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We study the long time behaviour of the heat kernel on Abelian covers of compact Riemannian manifolds. For manifolds without boundary work of Lott and Kotani-Sunada establishes precise long time asymptotics. Extending these results to manifolds with boundary reduces to a cute eigenvalue minimization problem, which we resolve for a Dirichlet and Neumann boundary conditions. We will show how these results can be applied to studying the winding'' / entanglement'' of Brownian trajectories in Riemannian manifolds.

• CategoryProbability
• Duration: 01:34:40
• Date:  April 19, 2018 at 3:10 PM
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