标题： 二维扩展过程中的定量重现 显示英文标题

标题： Quantitative recurrence in two-dimensional extended processes

摘要： 在一些温和的条件下，平面上的随机游走是常返的。 特别是每个轨迹都是稠密的，一个自然的问题是需要多少时间才能接近原点的一个小邻域。 我们在一些类似于平面随机游走的扩展动力系统的情况下解决这个问题，包括$\ZZ^2$-扩展的双曲动力学。 我们定义了一个逐点常返率，并将其与过程的维数相关联，建立了靠近原点的重访时间的分布收敛性。 显示英文摘要

摘要： 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.