%0 Journal Article
%T A Dirichlet principle for non reversible Markov chains and some recurrence theorems
%+ Institut de Mathématiques de Marseille (I2M)
%+ Instituto Nacional de Matemática Pura e Aplicada (IMPA)
%+ Laboratoire de Mathématiques Raphaël Salem (LMRS)
%A Gaudilliere, Alexandre
%A Landim, Claudio
%Z 27 pages
%< avec comité de lecture
%@ 0178-8051
%J Probability Theory and Related Fields
%I Springer Verlag
%V 158
%P 55-89
%8 2014
%D 2014
%K Recurrence
%K Markov process
%K Potential theory
%K Non-reversible
%K Dirichlet principle
%K Recurrence.
%Z Mathematics [math]/Probability [math.PR]Journal articles
%X 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 some recurrence theorems. In particular, we show the recurrence of two-dimensional cycle random walks under a second moment condition on the winding numbers.
%G English
%2 https://hal.science/hal-00648042/document
%2 https://hal.science/hal-00648042/file/gl2.pdf
%L hal-00648042
%U https://hal.science/hal-00648042
%~ LATP
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ LMRS
%~ I2M
%~ I2M-2014-
%~ COMUE-NORMANDIE
%~ UNIROUEN