Article,
Renormalization of the voter model in equilibrium
Ann. Probab., 29 (3): 1262--1302 (2001)
DOI: 10.1214/aop/1015345603
Abstract
We consider the d-dimensional voter model for d≥3. Our interest is the large scale limit of the equilibrium state of the voter model, where we prove the d=3 results of 1 for d≥4, which turn out to be of a different nature than for d=3. For this purpose we use the historical process.We establish some surprising facts about the Green’s function of random walks in dimension d≥4,which lead to the different features in d=3 versus d≥4. Secondly, we prove an analogous result for the voter model on the hierarchical group.
