Probability Theory and Related Fields

, Volume 72, Issue 2, pp 215–230

Simple random walk on the line in random environment

  • Paul Deheuvels
  • Pál Révész

DOI: 10.1007/BF00699104

Cite this article as:
Deheuvels, P. & Révész, P. Probab. Th. Rel. Fields (1986) 72: 215. doi:10.1007/BF00699104


We obtain strong limiting bounds for the maximal excursion and for the maximum reached by a random walk in a random environment. Our results derive from a simple proof of Pólya's theorem for the recurrence of the random walk on the line. As applications, we obtain bounds for the number of visits of the random walk at the origin.

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Paul Deheuvels
    • 1
  • Pál Révész
    • 2
    • 3
  1. 1.LSTA, t.45-55Université Paris VIParis Cedex 05France
  2. 2.Mathematical Institute of the Hungarian Academy of SciencesBudapest V.Hungary
  3. 3.Technische Universität WienWienAustria