Geodesic
Central Limit Theorem for a Class of Nonhomogeneous Random Walks
Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 751-757.

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A spatially nonhomogeneous random walk $\eta_t$ on the grid $\mathbb Z^\nu=\mathbb Z^m\times\mathbb Z^n$ is considered. Let $\eta_t^0$ be a random walk homogeneous in time and space, and let $\eta_t$ be obtained from it by changing transition probabilities on the set $A=\overline A\times\mathbb Z^n$, $|\overline A|\infty$, so that the walk remains homogeneous only with respect to the subgroup $\mathbb Z^n$ of the group $\mathbb Z^\nu$. It is shown that if $m\ge2$ or the drift is distinct from zero, then the central limit theorem holds for $\eta_t$. 
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D. A. Yarotskii. Central Limit Theorem for a Class of Nonhomogeneous Random Walks. Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 751-757. http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a10/

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