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university of Provence - Aix-Marseille I |  |
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university of Provence - Aix-Marseille I | |
| HAL: hal-00648042, version 1 |
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| A Dirichlet principle for non reversible Markov chains and some recurrence theorems |
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| Alexandre Gaudilliere 1, 2Claudio Landim 2, 3 |
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| (2011-11-09) |
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| 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. |
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| 1: | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| 2: | Instituto Nacional de Matemática Pura e Aplicada (IMPA) |
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Instituto Nacional de matematica pura e aplicada |
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| 3: | Laboratoire de Mathématiques Raphaël Salem (LMRS) |
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CNRS : UMR6085 – Université de Rouen |
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| Subject | : | Mathematics/Probability |
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| Markov process – Potential theory – Non-reversible – Dirichlet principle – Recurrence. |
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| hal-00648042, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00648042 | |
| oai:hal.archives-ouvertes.fr:hal-00648042 | |
| From: Alexandre Gaudilliere | |
| Submitted on: Monday, 5 December 2011 01:08:06 | |
| Updated on: Monday, 5 December 2011 08:46:59 | |
