%0 Generic %1 oliveira2010coalescence %A Oliveira, Roberto Imbuzeiro %D 2010 %K coalescent_theory coalescent_time probability_theory random_walks_on_graphs %T On the coalescence time of reversible random walks %U http://arxiv.org/abs/1009.0664 %X Consider a system of coalescing random walks where each individual performs random walk over a finite graph G, or (more generally) evolves according to some reversible Markov chain generator Q. Let C be the first time at which all walkers have coalesced into a single cluster. C is closely related to the consensus time of the voter model for this G or Q. We prove that the expected value of C is at most a constant multiple of the largest hitting time of an element in the state space. This solves a problem posed by Aldous and Fill and gives sharp bounds in many examples, including all vertex-transitive graphs. We also obtain results on the expected time until only k>1 clusters remain. Our proof tools include a new exponential inequality for the meeting time of a reversible Markov chain and a deterministic trajectory, which we believe to be of independent interest.

@misc{oliveira2010coalescence, abstract = {Consider a system of coalescing random walks where each individual performs random walk over a finite graph G, or (more generally) evolves according to some reversible Markov chain generator Q. Let C be the first time at which all walkers have coalesced into a single cluster. C is closely related to the consensus time of the voter model for this G or Q. We prove that the expected value of C is at most a constant multiple of the largest hitting time of an element in the state space. This solves a problem posed by Aldous and Fill and gives sharp bounds in many examples, including all vertex-transitive graphs. We also obtain results on the expected time until only k>1 clusters remain. Our proof tools include a new exponential inequality for the meeting time of a reversible Markov chain and a deterministic trajectory, which we believe to be of independent interest.}, added-at = {2013-10-21T19:06:43.000+0200}, author = {Oliveira, Roberto Imbuzeiro}, biburl = {https://www.bibsonomy.org/bibtex/23aeeed102e183b548b6428690622dfd2/peter.ralph}, interhash = {0fc839b947128c1c98682d6cd085f518}, intrahash = {3aeeed102e183b548b6428690622dfd2}, keywords = {coalescent_theory coalescent_time probability_theory random_walks_on_graphs}, timestamp = {2013-10-21T19:06:43.000+0200}, title = {On the coalescence time of reversible random walks}, url = {http://arxiv.org/abs/1009.0664}, year = 2010 }