The consensus times of the majority vote process on a torus

Abstract

We study the majority vote process on a two-dimensional torus in which every voter adopts the minority of opinion with small probability δ. We identify the exponent that the mean of consensus time is asymptotically (1/δ) with that exponent as δ 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.