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Mirror Coupling of Reflecting Brownian Motion and an Application to Chavel's Conjecture


 
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1. Title Title of document Mirror Coupling of Reflecting Brownian Motion and an Application to Chavel's Conjecture
 
2. Creator Author's name, affiliation, country Mihai N Pascu; Transilvania University of Brasov; Romania
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) couplings, mirror coupling, reflecting Brownian motion, Chavel's conjecture
 
3. Subject Subject classification 60J65; 60H20; 35K05; 60H30
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) The author kindly acknowledges the support from CNCSIS-UEFISCSU research grant PNII - IDEI 209/2007.
 
7. Date (YYYY-MM-DD) 2011-03-17
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/859
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-859
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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