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 neighbourhood of the origin. We address this question in the case of some extended dynamical systems similar to planar random walks, including ℤ2-extension of mixing subshifts of finite type. We define a pointwise recurrence rate and relate it to the dimension of the process, and establish a result of convergence in distribution of the rescaled return time near the origin.
Publié le : 2009-11-15
Classification:
Return time,
Random walk,
Subshift of finite type,
Recurrence,
Local limit theorem,
37B20,
37A50,
60Fxx
@article{1257529892,
author = {P\`ene, Fran\c coise and Saussol, Beno\^\i t},
title = {Quantitative recurrence in two-dimensional extended processes},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {45},
number = {1},
year = {2009},
pages = { 1065-1084},
language = {en},
url = {http://dml.mathdoc.fr/item/1257529892}
}
Pène, Françoise; Saussol, Benoît. Quantitative recurrence in two-dimensional extended processes. Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, pp. 1065-1084. http://gdmltest.u-ga.fr/item/1257529892/