On the limiting velocity of random walks in mixing random environment

Xiaoqin Guo

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 2, page 375-402
  • ISSN: 0246-0203

Abstract

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We consider random walks in strong-mixing random Gibbsian environments in ℤ d , d ≥ 2 . Based on regeneration arguments, we will first provide an alternative proof of Rassoul-Agha’s conditional law of large numbers (CLLN) for mixing environment (Electron. Commun. Probab.10(2005) 36–44). Then, using coupling techniques, we show that there is at most one nonzero limiting velocity in high dimensions ( d ≥ 5 ).

How to cite

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Guo, Xiaoqin. "On the limiting velocity of random walks in mixing random environment." Annales de l'I.H.P. Probabilités et statistiques 50.2 (2014): 375-402. <http://eudml.org/doc/272047>.

@article{Guo2014,
abstract = {We consider random walks in strong-mixing random Gibbsian environments in $\mathbb \{Z\}^\{d\}$, $d\ge 2$. Based on regeneration arguments, we will first provide an alternative proof of Rassoul-Agha’s conditional law of large numbers (CLLN) for mixing environment (Electron. Commun. Probab.10(2005) 36–44). Then, using coupling techniques, we show that there is at most one nonzero limiting velocity in high dimensions ($d\ge 5$).},
author = {Guo, Xiaoqin},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random walks; random environment; mixing; limiting speed; conditional law of large numbers; random walk},
language = {eng},
number = {2},
pages = {375-402},
publisher = {Gauthier-Villars},
title = {On the limiting velocity of random walks in mixing random environment},
url = {http://eudml.org/doc/272047},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Guo, Xiaoqin
TI - On the limiting velocity of random walks in mixing random environment
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 2
SP - 375
EP - 402
AB - We consider random walks in strong-mixing random Gibbsian environments in $\mathbb {Z}^{d}$, $d\ge 2$. Based on regeneration arguments, we will first provide an alternative proof of Rassoul-Agha’s conditional law of large numbers (CLLN) for mixing environment (Electron. Commun. Probab.10(2005) 36–44). Then, using coupling techniques, we show that there is at most one nonzero limiting velocity in high dimensions ($d\ge 5$).
LA - eng
KW - random walks; random environment; mixing; limiting speed; conditional law of large numbers; random walk
UR - http://eudml.org/doc/272047
ER -

References

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  12. [12] O. Zeitouni. Random walks in random environment. In Lectures on Probability Theory and Statistics 189–312. Lecture Notes in Math. 1837. Springer, Berlin, 2004. Zbl1060.60103MR2071631
  13. [13] M. Zerner. A non-ballistic law of large numbers for random walks in i.i.d. random environment. Electron. Commun. Probab.7 (2002) 191–197. Zbl1008.60107MR1937904
  14. [14] M. Zerner and F. Merkl. A zero-one law for planar random walks in random environment. Ann. Probab.29 (2001) 1716–1732. Zbl1016.60093MR1880239

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