Weak quenched limiting distributions for transient one-dimensional random walk in a random environment

Details Weak quenched limiting distributions for transient one-dimensional random walk in a random environment Weak quenched limiting distributions for transient one-dimensional random walk in a random environment

2010-11-29

arxiv.org/abs/1011.6366v3

Mathematics

Probability

Changed the statement and proof of Corollary 1.8 (previously Corollary 1.7) to correct an error in the previous version

Scientific paper

We consider a one-dimensional, transient random walk in a random i.i.d. environment. The asymptotic behaviour of such random walk depends to a large extent on a crucial parameter $\kappa>0$ that determines the fluctuations of the process. When $0<\kappa<2$, the averaged distributions of the hitting times of the random walk converge to a $\kappa$-stable distribution. However, it was shown recently that in this case there does not exist a quenched limiting distribution of the hitting times. That is, it is not true that for almost every fixed environment, the distributions of the hitting times (centered and scaled in any manner) converge to a non-degenerate distribution. We show, however, that the quenched distributions do have a limit in the weak sense. That is, the quenched distributions of the hitting times -- viewed as a random probability measure -- converge in distribution to a random probability measure, which has interesting stability properties. Our results generalize both the averaged limiting distribution and the non-existence of quenched limiting distributions.

Affiliated with

Also associated with

No associations

Rating

Weak quenched limiting distributions for transient one-dimensional random walk in a random environment does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Weak quenched limiting distributions for transient one-dimensional random walk in a random environment, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weak quenched limiting distributions for transient one-dimensional random walk in a random environment will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-443750