Abstract
We construct a sequence of transient random walks in random environments and prove that by proper scaling, it converges to a diffusion process with drifted Brownian potential. To this end, we prove a counterpart of convergence for transient random walk in non-random environment, which is interesting itself.
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Acknowledgements
The authors thank the anonymous referees for their very careful reading of the manuscript. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11531001, 11626245) and the Fundamental Research Funds for the Central Universities of Minzu University of China (Grant No. 2017QNPY30).
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Hong, W., Yang, H. Scaling limit theorem for transient random walk in random environment. Front. Math. China 13, 1033–1044 (2018). https://doi.org/10.1007/s11464-018-0723-y
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DOI: https://doi.org/10.1007/s11464-018-0723-y