On the coalescence time of reversible random walks

By Roberto Imbuzeiro Oliveira. 2010

62 citations recorded by the source corpus.

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 � 2 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.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4ece3641754fdb2cd8833c7f577df191b4e7ed68

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In Mathematical Physics

In Statistical and Nonlinear Physics

Roberto Imbuzeiro Oliveira

In Statistics and Probability

Citations in the corpus

Mean field conditions for coalescing random walks (2011, methodology): “For the reversible/transitive case, we use a bound from [14] which is of the optimal order.”