Electronic Communications in Probability

A Non-Ballistic Law of Large Numbers for Random Walks in I.I.D. Random Environment

Martin Zerner

Full-text: Open access

PDF File (191 KB)

Abstract

We prove that random walks in i.i.d. random environments which oscillate in a given direction have velocity zero with respect to that direction. This complements existing results thus giving a general law of large numbers under the only assumption of a certain zero-one law, which is known to hold if the dimension is two.

Article information

Source
Electron. Commun. Probab., Volume 7 (2002), paper no. 19, 191-197.

Dates
Accepted: 30 September 2002
First available in Project Euclid: 16 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1463434786

Digital Object Identifier
doi:10.1214/ECP.v7-1060

Mathematical Reviews number (MathSciNet)
MR1937904

Zentralblatt MATH identifier
1008.60107

Subjects
Primary: 60K37: Processes in random environments
Secondary: 60F15: Strong theorems

Keywords
Random walk in random environment RWRE law of large numbers

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Zerner, Martin. A Non-Ballistic Law of Large Numbers for Random Walks in I.I.D. Random Environment. Electron. Commun. Probab. 7 (2002), paper no. 19, 191--197. doi:10.1214/ECP.v7-1060. https://projecteuclid.org/euclid.ecp/1463434786


Export citation

References

  • Sznitman, A.-S. (2002), Topics in Random Walks in Random Environments. http://www.math.ethz.ch/~sznitman/topics-paper.pdf (preprint)
  • Sznitman, A.-S. and Zerner, M.P.W. (1999), A law of large numbers for random walks in random environment. Ann. Probab. 27, no. 4, 1851-1869
    Zentralblatt MATH: 0965.60100
    Digital Object Identifier: doi:10.1214/aop/1022874818
    Project Euclid: euclid.aop/1022874818
  • Zeitouni, O. (2001), Notes on Saint Flour Lectures 2001. http://www.ee.technion.ac.il/~zeitouni/ps/notes1.ps (preprint)
  • Zerner, M.P.W. and Merkl, F. (2001), A zero-one law for planar random walks in random environment. Ann. Probab. 29, No. 4, 1716-1732
    Zentralblatt MATH: 1016.60093
    Digital Object Identifier: doi:10.1214/aop/1015345769
    Project Euclid: euclid.aop/1015345769

The Institute of Mathematical Statistics and the Bernoulli Society

Electronic Communications in Probability

New content alerts

Email RSS ToC RSS Article
  • You have access to this content.
  • You have partial access to this content.
  • You do not have access to this content.
Turn Off MathJax

What is MathJax?

More like this

+ See more