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Journal Article

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

Erwin Bolthausen
The Annals of Probability
Vol. 17, No. 1 (Jan., 1989), pp. 108-115
Stable URL: http://www.jstor.org/stable/2244199
Page Count: 8

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Topics: Central limit theorem, Random walk, Random variables, Mathematical moments, Preprints
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## Abstract

Let Sn, n ∈ N, be a recurrent random walk on Z2 (S0 = 0) and ξ(α), α ∈ Z2, be i.i.d. 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.

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