Bolthausen, Erwin A central limit theorem for two-dimensional random walks in random sceneries. (English) Zbl 0679.60028 Ann. Probab. 17, No. 1, 108-115 (1989). 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 Cited in 39 Documents 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 × Cite Format Result Cite Review PDF Full Text: DOI