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

作者：Gaudilliere A; Landim C^*

来源：Probability Theory and Related Fields, 2014, 158(1-2): 55-89.

DOI：10.1007/s00440-012-0477-5

• Markov process
• Potential theory
• Non-reversible
• Dirichlet principle
• Recurrence

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.

• 出版日期2014-2