Open Access
Translator Disclaimer
February, 1975 Random Walks in a Random Environment
Fred Solomon
Ann. Probab. 3(1): 1-31 (February, 1975). DOI: 10.1214/aop/1176996444


Let $\{\alpha_n\}$ be a sequence of independent, identically distributed random variables with $0 \leqq \alpha_n \leqq 1$ for all $n$. The random walk in a random environment on the integers is the sequence $\{X_n\}$ where $X_0 = 0$ and inductively $X_{n+1} = X_n + 1, (X_n - 1)$, with probability $\alpha_{X_n}, (1 - \alpha_{X_n})$. In this paper we consider limit theorems for the random walk in a random environment. We show that "randomizing the environment" in some sense "slows down" the random walk in Section One. The remaining sections are concerned with features of this "slowing down" in some simple models.


Download Citation

Fred Solomon. "Random Walks in a Random Environment." Ann. Probab. 3 (1) 1 - 31, February, 1975.


Published: February, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0305.60029
MathSciNet: MR362503
Digital Object Identifier: 10.1214/aop/1176996444

Keywords: 60.30 , 60.66 , difference equation with random coefficients , diffusion , Markov chains , Random walk

Rights: Copyright © 1975 Institute of Mathematical Statistics


Vol.3 • No. 1 • February, 1975
Back to Top