Variance limite d'une marche aléatoire réversible en milieu aléatoire sur Z (Limit of the Variance of a Reversible Random Walk in Random Medium on Z) - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2009

Variance limite d'une marche aléatoire réversible en milieu aléatoire sur Z (Limit of the Variance of a Reversible Random Walk in Random Medium on Z)

Résumé

The Central Limit Theorem for the random walk on a stationary random network of conductances has been studied by several authors. In one dimension, when conductances and resistances are integrable, and following a method of martingale introduced by S. Kozlov (1985), we can prove the Quenched Central Limit Theorem. In that case the variance of the limit law is not null. When resistances are not integrable, the Annealed Central Limit Theorem with null variance was established by Y. Derriennic and M. Lin (personal communication). The quenched version of this last theorem is proved here, by using a very simple method. The similar problem for the continuous diffusion is then considered. Finally our method allows us to prove an inequality for the quadratic mean of a diffusion (X_t)_t at all time t.
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Dates et versions

hal-00358363 , version 1 (03-02-2009)

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Jérôme Depauw, Jean-Marc Derrien. Variance limite d'une marche aléatoire réversible en milieu aléatoire sur Z (Limit of the Variance of a Reversible Random Walk in Random Medium on Z). 2009. ⟨hal-00358363⟩
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