Pré-Publication, Document De Travail Année : 2007

Quantitative recurrence in two-dimensional extended processes

Résumé

Under some mild condition, a random walk in the plane is recurrent. In particular each trajectory is dense, and a natural question is how much time one needs to approach a given small neighborhood of the origin. We address this question in the case of some extended dynamical systems similar to planar random walks, including $\ZZ^2$-extension of hyperbolic dynamics. We define a pointwise recurrence rate and relate it to the dimension of the process, and establish a convergence in distribution of the rescaled return times near the origin.

Fichier principal
Vignette du fichier
qrecplane.pdf (273.99 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-00172430 , version 1 (17-09-2007)

Licence

Identifiants

Citer

Françoise Pene, Benoit Saussol. Quantitative recurrence in two-dimensional extended processes. 2007. ⟨hal-00172430⟩
168 Consultations
213 Téléchargements

Altmetric

Partager

  • More