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2006 Hot-spots for conditioned Brownian motion
Rodrigo Bañuelos, Pedro J. Méndez-Hernández
Illinois J. Math. 50(1-4): 1-32 (2006). DOI: 10.1215/ijm/1258059468

Abstract

Let $D$ be a bounded domain in the plane which is symmetric and convex with respect to both coordinate axes. We prove that the Brownian motion conditioned to remain forever in $D$, the Doob $h$-process where $h$ is the ground state Dirichlet eigenfunction in $D$, has the "hot-spots" property. That is, the first non-constant eigenfunction corresponding to the semigroup of this process with its nodal line on one of the coordinate axes attains its maximum and minimum on the boundary and only on the boundary of the domain. This is the exact analogue for conditioned Brownian motion of the result in \cite{JN} for Neumann eigenfunctions.

Citation

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Rodrigo Bañuelos. Pedro J. Méndez-Hernández. "Hot-spots for conditioned Brownian motion." Illinois J. Math. 50 (1-4) 1 - 32, 2006. https://doi.org/10.1215/ijm/1258059468

Information

Published: 2006
First available in Project Euclid: 12 November 2009

zbMATH: 1106.47015
MathSciNet: MR2247822
Digital Object Identifier: 10.1215/ijm/1258059468

Subjects:
Primary: 60J45
Secondary: 35J10, 47A75

Rights: Copyright © 2006 University of Illinois at Urbana-Champaign

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Vol.50 • No. 1-4 • 2006
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