Geodesic
A criterion for linear drift, and the~central limit theorem for one-dimensional random walks in a~random environment
Sbornik. Mathematics, Tome 79 (1994) no. 1, pp. 73-92

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A study is made of one-dimensional random walks in a random environment with bounded jumps in a unit of time (no more than $L$ to the left and no more than $R$ to the right, where $R$ and $L$ are positive integers). A criterion for linear drift is proved, along with the central limit theorem for such random walks in a random environment. 
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     author = {A. V. Letchikov},
     title = {A criterion for linear drift, and the~central limit theorem for one-dimensional random walks in a~random environment},
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A. V. Letchikov. A criterion for linear drift, and the~central limit theorem for one-dimensional random walks in a~random environment. Sbornik. Mathematics, Tome 79 (1994) no. 1, pp. 73-92. http://geodesic.mathdoc.fr/item/SM_1994_79_1_a5/