Mirror couplings and Neumann eigenfunctions

被引：4

作者：

Atar, Rami ^{[1
]}

Burdzy, Krzysztof ^{[2
]}

机构：

[1] Technion Israel Inst Technol, Dept Elect Engn, IL-32000 Haifa, Israel

[2] Univ Washington, Seattle, WA 98195 USA

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2008年 / 57卷 / 03期

关键词：

Neumann eigenfunctions; reflected Brownian motion; couplings;

D O I：

10.1512/iumj.2008.57.3222

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We analyze a pair of reflected Brownian motions in a planar domain D, for which the increments of both processes form mirror images of each other when the processes are not on the boundary. We show that for D in a class of smooth convex planar domains, the two processes remain ordered forever, according to a certain partial order. This is used to prove that the second eigenvalue is simple for the Laplacian with Neumann boundary conditions for the same class of domains.

引用

页码：1317 / 1351

页数：35

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