Mirror couplings and Neumann eigenfunctions
نویسندگان
چکیده
منابع مشابه
Mirror Couplings and Neumann Eigenfunctions
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 t...
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2008
ISSN: 0022-2518
DOI: 10.1512/iumj.2008.57.3222