The Annals of Probability

A Central Limit Theorem for Two-Dimensional Random Walks in Random Sceneries

Erwin Bolthausen

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Abstract

Let $S_n, n \in \mathbb{N}$, be a recurrent random walk on $\mathbb{Z}^2 (S_0 = 0)$ and $\xi(\alpha), \alpha \in \mathbb{Z}^2$, be i.i.d. $\mathbb{R}$-valued centered random variables. It is shown that $\sum^n_{i = 1}\xi(S_i)/ \sqrt{n \log n}$ satisfies a central limit theorem. A functional version is presented.

Article information

Source
Ann. Probab., Volume 17, Number 1 (1989), 108-115.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991497

Digital Object Identifier
doi:10.1214/aop/1176991497

Mathematical Reviews number (MathSciNet)
MR972774

Zentralblatt MATH identifier
0679.60028

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60J15 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Random walk random scenery central limit theorem

Citation

Bolthausen, Erwin. A Central Limit Theorem for Two-Dimensional Random Walks in Random Sceneries. Ann. Probab. 17 (1989), no. 1, 108--115. doi:10.1214/aop/1176991497. https://projecteuclid.org/euclid.aop/1176991497


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