A Dirichlet principle for non reversible Markov chains and some recurrence theorems
By Alexandre Gaudilliere, C. Landim. 2011
84 citations recorded by the source corpus.
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.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/3673c4c434bb31199dd95020f09515aef3563db2
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In Mathematical Physics
- David A. Levin
- Yuval Peres
- Julien Reygner
- Freddy Bouchet
- Pablo Shmerkin
- Michael Hochman
- M. Kassmann
- Takashi Kumagai
In Statistics and Probability
- David A. Levin
- Yuval Peres
- Julien Reygner
- Freddy Bouchet
- Manjunath Krishnapur
- M. Kassmann
- Takashi Kumagai
- Terence Tao
Citations in the corpus
- Markov Chains and Mixing Times: Second Edition (2017, background): “Gheissari and Lubetzky (2016) analyze the critical case on Z(2)n. See Cuff, Ding, Louidor, Lubetzky, Peres, and Sly (2012) for the full story on the complete graph.”
- Generalisation of the Eyring–Kramers Transition Rate Formula to Irreversible Diffusion Processes (2015, methodology): “We finally recall that in the reversible case, the first proof of the Eyring– Kramers formula was obtained by means of potential theory [16] rather than WKB analysis, and mention that an extension of this theory to irreversible Markov processes was recently developed in [25], which then permitted to”