2007/09/17 by Pène, Françoise, Saussol, Benoit
#37B20 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.0709.2597
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 \ZZ2-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.