Quantitative recurrence in two-dimensional extended processes

Françoise Pène; Benoît Saussol

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 4, page 1065-1084
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Pène, Françoise, and Saussol, Benoît. "Quantitative recurrence in two-dimensional extended processes." Annales de l'I.H.P. Probabilités et statistiques 45.4 (2009): 1065-1084. <http://eudml.org/doc/78053>.

@article{Pène2009,
abstract = {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.},
author = {Pène, Françoise, Saussol, Benoît},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {return time; random walk; subshift of finite type; recurrence; local limit theorem},
language = {eng},
number = {4},
pages = {1065-1084},
publisher = {Gauthier-Villars},
title = {Quantitative recurrence in two-dimensional extended processes},
url = {http://eudml.org/doc/78053},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Pène, Françoise
AU - Saussol, Benoît
TI - Quantitative recurrence in two-dimensional extended processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 4
SP - 1065
EP - 1084
AB - 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.
LA - eng
KW - return time; random walk; subshift of finite type; recurrence; local limit theorem
UR - http://eudml.org/doc/78053
ER -

References

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