Abstract
We consider a random walk on the one-dimensional semi-lattice ℤ={0, 1, 2,...}. We prove that the moving particle walks mainly in a finite neighbourhood of a point depending only on time and a realization of the random environment. The size of this neighbourhood is estimated. The limit parameters of the walks are also determined.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Sinai, Ya. G.: Limit behaviour of one-dimensional random walk in random environment. Theory Probab. Appl.27, No. 2, 247–258 (1982) (in Russian)
Golosov, A.O.: Limit distributions for random walks in random environments. Dokl. Acad. Sci. USSR271, 25–29 (1983) (in Russian)
Feller, W.: An introduction to probability theory and its applications, Vol. 2. New York, London, Sydney: Wiley 1966
Billingsley, P.: Convergence of probability measures. New York, London, Sydney, Toronto: Wiley 1968
Pitman, J.W.: One-dimensional Brownian motion and the three-dimensional Bessel process. Adv. Appl. Probab.7, 511–526 (1975)
Author information
Authors and Affiliations
Additional information
Communicated by Ya. G. Sinai
Rights and permissions
About this article
Cite this article
Golosov, A.O. Localization of random walks in one-dimensional random environments. Commun.Math. Phys. 92, 491–506 (1984). https://doi.org/10.1007/BF01215280
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01215280