Optimal co-adapted coupling for a random walk on the hyper-complete-grap

Details Optimal co-adapted coupling for a random walk on the hyper-complete-grap Optimal co-adapted coupling for a random walk on the hyper-complete-grap

2009-08-14

arxiv.org/abs/0908.2038v1

Mathematics

Probability

16 pages

Scientific paper

Let $G_d$ be the complete graph with d vertices, and let X and Y be two simple symmetric continuous-time random walks on the vertices of $G_d^n$. When d=2, X and Y are random walks on the hypercube, for which a stochastically fastest co-adapted coupling is described by Connor & Jacka (2008). Here we extend this result to random walks on $G_d^n$, once again producing a stochastically optimal coupling: as d tends to infinity we show that this optimal co-adapted coupling tends to a maximal coupling.

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