Roitershtein, Alexander A log-scale limit theorem for one-dimensional random walks in random environments. (English) Zbl 1111.60082 Electron. Commun. Probab. 10, 244-253 (2005). Summary: We consider a transient one-dimensional random walk \(X_n\) in random environment having zero asymptotic speed. For a class of non-i.i.d. environments we show that \(\log X_n/\log n\) converges in probability to a positive constant. MSC: 60K37 Processes in random environments 60F05 Central limit and other weak theorems 60F10 Large deviations × Cite Format Result Cite Review PDF Full Text: DOI arXiv EuDML