THE CONSENSUS TIMES OF THE MAJORITY VOTE PROCESS ON A TORUS

摘要

We study the majority vote process on a two-dimensional torus in which every voter adopts the minority of opinion with small probability delta. We identify the exponent that the mean of consensus time is asymptotically (1/delta) with that exponent as delta goes to 0. The proof is by a formula for mean exit time and by the metastable theory of Markov chains developed in the study of the stochastic Ising model. [References: 16]