%0 Journal Article
%T Quantitative recurrence in two-dimensional extended processes
%A Fran£żoise P¨¨ne
%A Benoit Saussol
%J Mathematics
%D 2007
%I arXiv
%X 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.
%U http://arxiv.org/abs/0709.2597v1