A variation on the Donsker-Varadhan inequality for the principal eigenvalue.

Published

Journal Article

The purpose of this short paper is to give a variation on the classical Donsker-Varadhan inequality, which bounds the first eigenvalue of a second-order elliptic operator on a bounded domain Ω by the largest mean first exit time of the associated drift-diffusion process via [Formula: see text]Instead of looking at the mean of the first exit time, we study quantiles: let [Formula: see text] be the smallest time t such that the likelihood of exiting within that time is p, then [Formula: see text]Moreover, as [Formula: see text], this lower bound converges to λ1.

Full Text

Duke Authors

Cited Authors

  • Lu, J; Steinerberger, S

Published Date

  • August 23, 2017

Published In

Volume / Issue

  • 473 / 2204

Start / End Page

  • 20160877 -

PubMed ID

  • 28878551

Pubmed Central ID

  • 28878551

Electronic International Standard Serial Number (EISSN)

  • 1471-2946

International Standard Serial Number (ISSN)

  • 1364-5021

Digital Object Identifier (DOI)

  • 10.1098/rspa.2016.0877

Language

  • eng