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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
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