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# Variance limite d'une marche aléatoire réversible en milieu aléatoire sur ZZ

Comptes Rendus Mathematique (Impact Factor: 0.43). 04/2009; 347(s 7–8):401–406. DOI: 10.1016/j.crma.2009.01.030
Source: arXiv

ABSTRACT 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. To cite this article: J. Depauw, J.-M. Derrien, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

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##### Article: Sur les lois de chaînes de Markov duales sur Z
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ABSTRACT: On établit une formule de correspondance entre les lois de chaînes de Markov \flqq duales\frqq\$\ \$ sur \$\Z\$. Cette formule apporte une contribution à l'étude des marches aléatoires en milieu aléatoire stationnaire.