@article{EJP859,
author = {Mihai Pascu},
title = {Mirror Coupling of Reflecting Brownian Motion and an Application to Chavel's Conjecture},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {16},
year = {2011},
keywords = {couplings, mirror coupling, reflecting Brownian motion, Chavel's conjecture},
abstract = {In a series of papers, Burdzy et al. introduced the mirror coupling of reflecting Brownian motions in a smooth bounded domain $D\subset\mathbb{R}^d$, and used it to prove certain properties of eigenvalues and eigenfunctions of the Neumann Laplacian on $D$. In the present paper we show that the construction of the mirror coupling can be extended to the case when the two Brownian motions live in different domains $D_1, D_2\subset\mathbb{R}^d$. As applications of the construction, we derive a unifying proof of the two main results concerning the validity of Chavel's conjecture on the domain monotonicity of the Neumann heat kernel, due to I. Chavel ([12]), respectively W. S. Kendall ([16]), and a new proof of Chavel's conjecture for domains satisfying the ball condition, such that the inner domain is star-shaped with respect to the center of the ball.},
pages = {no. 18, 504-530},
issn = {1083-6489},
doi = {10.1214/EJP.v16-859},
url = {http://ejp.ejpecp.org/article/view/859}}