Exit Time Moments and Eigenvalue Estimates

Authors

Jeffrey J. Langford, Bucknell UniversityFollow
Emily Dryden, Bucknell UniversityFollow
Patrick McDonald, New College of Florida

Publication Date

2017

Description

We give upper bounds on the principal Dirichlet eigenvalue associated to a smoothly bounded domain in a complete Riemannian manifold; the bounds involve L1L1‐norms of exit time moments of Brownian motion. Our results generalize a classical inequality of Pólya. We also prove lower bounds for Dirichlet eigenvalues using invariants that arise during the examination of the relationship between the heat content and exit time moments.

Journal

Bulletin of the London Mathematical Society

Volume

49

Issue

3

First Page

480

Last Page

490

Department

Mathematics

Recommended Citation

Langford, Jeffrey J.; Dryden, Emily; and McDonald, Patrick. "Exit Time Moments and Eigenvalue Estimates." Bulletin of the London Mathematical Society (2017) : 480-490.