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| HAL: hal-00368275, version 1 |
| arXiv: 0903.2696 |
| Detailed view |  Export this paper |
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| The local time of a random walk on growing hypercubes |
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| Pierre Andreoletti 1 |
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| (2009-03) |
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| We study a random walk in a random environment (RWRE) on $\Z^d$, $1 \leq d < +\infty$. The main assumptions are that conditionned on the environment the random walk is reversible. Moreover we construct our environment in such a way that the walk can't be trapped on a single point like in some particular RWRE but in some specific d-1 surfaces. These surfaces are basic surfaces with deterministic geometry. We prove that the local time in the neighborhood of these surfaces is driven by a function of the (random) reversible measure. As an application we get the limit law of the local time as a process on these surfaces. |
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| 1: | Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO) |
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Université d'Orléans – CNRS : UMR7349 |
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| Subject | : | Mathematics/Probability |
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| random environment – reversible markov chain – Dirichlet method – recurrent regime – local time |
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| hal-00368275, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00368275 | |
| oai:hal.archives-ouvertes.fr:hal-00368275 | |
| From: Pierre Andreoletti | |
| Submitted on: Sunday, 15 March 2009 22:21:04 | |
| Updated on: Monday, 16 March 2009 06:27:30 | |
