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A central limit theorem for two-dimensional random walks in random sceneries. (English) Zbl 0679.60028
This paper is concerned with a random walk $$\{S_ n$$, $$n\in N\}$$ on $$Z^ 2$$ whose increments are i.i.d. with zero mean vector and finite covariance matrix and a random scenery $$\xi$$ ($$\alpha)$$, $$\alpha \in Z^ 2$$, the $$\xi$$ ’s being i.i.d. with zero mean and finite variance.
It is shown that $$\sum^{n}_{i=1}\xi (S_ i)/(n \log n)^{1/2}$$ satisfies a central limit theorem. A functional version is also presented.
Reviewer: C.C.Heyde

##### MSC:
 60F05 Central limit and other weak theorems 60G50 Sums of independent random variables; random walks 60K35 Interacting random processes; statistical mechanics type models; percolation theory
##### Keywords:
random scenery; random walk; central limit theorem
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