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What if A is in (4,x), B in (5,y), and A goes right? As far as I understood, B shall go left, so that A and B horizontal coordinates crosses. If initially A=(0,0) and B=(10,10), then it's ok, but if B has odd coordinates, then A and B never meet, right?...
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Does it deserve to be mentionned that the first occurence of coupling in probability theory seems to be the proof of convergence to the stationary distribution of a Markov chain by
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