We consider random walks on in a random medium with {−L,…,−1,0,+1} as possible jumps, where L⩾1 is fixed. When the environment is defined by a Gibbs measure on a subshift of finite type, we show a dichotomy in the recurrent case between the pointwise functional CLT and the slow behavior described by Sinaï. In the transient cases and under natural integrability conditions, we prove the validity of the averaged CLT.
Nous étudions des marches aléatoires sur en milieu aléatoire avec {−L,…,−1,0,+1} comme sauts possibles, où L⩾1 est fixé. Pour un environnement défini par une mesure de Gibbs sur un sous-shift de type fini, nous montrons dans le cas récurrent une dichotomie entre le TCL fonctionnel ponctuel et le comportement lent décrit par Sinaï. Dans les cas transients et sous des conditions d'intégrabilité naturelles, nous montrons la validité du TCL en moyenne.
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Julien Bremont 1
@article{CRMATH_2004__338_11_895_0, author = {Julien Bremont}, title = {Behavior of random walks on $ \mathbb{Z}$ in {Gibbsian} medium}, journal = {Comptes Rendus. Math\'ematique}, pages = {895--898}, publisher = {Elsevier}, volume = {338}, number = {11}, year = {2004}, doi = {10.1016/j.crma.2004.03.030}, language = {en}, }
Julien Bremont. Behavior of random walks on $ \mathbb{Z}$ in Gibbsian medium. Comptes Rendus. Mathématique, Volume 338 (2004) no. 11, pp. 895-898. doi : 10.1016/j.crma.2004.03.030. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.030/
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