Quantitative recurrence in two-dimensional extended processes

Details Quantitative recurrence in two-dimensional extended processes Quantitative recurrence in two-dimensional extended processes

2007-09-17

arxiv.org/abs/0709.2597v1

Mathematics

Dynamical Systems

Scientific paper

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.

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