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Shy couplings

Itai Benjamini·Krzysztof Burdzy·Zhen-Qing Chen
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Abstract

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 ``shy'' if the processes never come closer than some (random) strictly positive distance from each other. We investigate whether shy couplings exist for several classes of Markov processes.

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Itai Benjamini, Krzysztof Burdzy, Zhen-Qing Chen. 2005-09-20. Shy couplings. https://arxiv.org/abs/math/0509458

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