Math @ Duke

Publications [#328895] of Jianfeng Lu
Papers Published
 Lu, J; Steinerberger, S, A variation on the DonskerVaradhan inequality for the principal eigenvalue.,
Proceedings. Mathematical, Physical, and Engineering Sciences, vol. 473 no. 2204
(August, 2017),
pp. 20160877 [doi]
(last updated on 2018/10/16)
Abstract: The purpose of this short paper is to give a variation on the classical DonskerVaradhan inequality, which bounds the first eigenvalue of a secondorder elliptic operator on a bounded domain Ω by the largest mean first exit time of the associated driftdiffusion 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.


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