A Dirichlet principle for non reversible Markov chains and some recurrence theorems

• 成果类型: Article
• 署名作者: Gaudilliere, A.; Landim, C.
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0477-5
• 发表日期: 2014
• 页码: 55-89
• 关键词: random-walks; random-environments; diffusion; metastability

摘要

We extend the Dirichlet principle to non-reversible Markov processes on countable state spaces. We present two variational formulas for the solution of the Poisson equation or, equivalently, for the capacity between two disjoint sets. As an application we prove a some recurrence theorems. In particular, we show the recurrence of two-dimensional cycle random walks under a second moment condition on the winding numbers.