Winding of Brownian trajectories and heat kernels on covering spaces

Probability Seminar

Gautam Iyer (Carnegie Mellon)

Thursday, April 19, 2018 -
3:15pm to 4:15pm
119 Physics

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.

Last updated: 2019/04/23 - 6:13am