3 papers
math.PR2005
Shy couplings
Itai Benjamini, Krzysztof Burdzy, Zhen-Qing Chen
A pair of Markov processes is called a Markov coupling if both processes have the same transition probabilities and the pair is also a Markov process. We say that a coupling is ``s…
math.PR2005
Synchronous couplings of reflected Brownian motions in smooth domains
Krzysztof Burdzy, Zhen-Qing Chen, Peter Jones
For every bounded planar domain with a smooth boundary, we define a `Lyapunov exponent' using a fairly explicit formula. We consider two reflected Brownian motions in $D…
math.AP2004
The "hot spots" problem in planar domains with one hole
Krzysztof Burdzy
There exists a planar domain with piecewise smooth boundary and one hole such that the second eigenfunction for the Laplacian with Neumann boundary conditions attains its maximum a…