Renormalization of the voter model in equilibrium

• 成果类型: Article
• 署名作者: Zähle, I
• 署名单位: University of Erlangen Nuremberg
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1015345603
• 发表日期: 2001
• 页码: 1262-1302
• 关键词: interacting diffusions; cluster-formation

摘要

We consider the d-dimensional voter model for d greater than or equal to 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 greater than or equal to 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.