Winding of Brownian trajectories and heat kernels on covering spaces

Winding of Brownian trajectories and heat kernels on covering spaces

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Gautam Iyer, Carnegie Mellon University
Fine Hall 322

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" of Brownian trajectories in Riemannian manifolds.