Shy couplings
  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. 
Itai Benjamini, Krzysztof Burdzy and Zhen-Qing Chen