期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2015
卷号：XII
页码：357-374
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We study a continuous time Markov process whose state space consistsof an assignment of +1 or 1 to each vertex of a graph G. The graphs that we treatare related to homogeneous trees of degree K 3, such as nite or in nite stacksof such trees. The initial spin con guration is chosen from a Bernoulli productmeasure with density of +1 spins. The system evolves according to an agreementinducing dynamics: each vertex, at rate 1, changes its spin value to agree withthe majority of its neighbors. We study the long time behavior of this systemand prove that, if is close enough to 1, the system reaches xation to consensus.The geometric percolation-type arguments introduced here may be of independentinterest.
