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This article is cited in 1 scientific paper (total in 1 paper)
Random walk in mixed random environment without uniform ellipticity
Ostap Hryniv, Mikhail V. Menshikov, Andrew R. Wade Department of Mathematical Sciences, Durham University, Durham, UK
Abstract:
We study a random walk in random environment on $\mathbb Z_+$. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i) points endowed with probabilities drawn from a symmetric distribution with heavy tails at 0 and 1, and (ii) “fast points” with a fixed systematic drift. Without these fast points, the model is related to the diffusion in heavy-tailed (“stable”) random potential studied by Schumacher and Singh; the fast points perturb that model. The two components compete to determine the behaviour of the random walk; we identify phase transitions in terms of the model parameters. We give conditions for recurrence and transience and prove almost sure bounds for the trajectories of the walk.
Received in February 2013
Citation:
Ostap Hryniv, Mikhail V. Menshikov, Andrew R. Wade, “Random walk in mixed random environment without uniform ellipticity”, Branching processes, random walks, and related problems, Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 282, MAIK Nauka/Interperiodica, Moscow, 2013, 114–131; Proc. Steklov Inst. Math., 282 (2013), 106–123
Linking options:
https://www.mathnet.ru/eng/tm3478https://doi.org/10.1134/S0371968513030102 https://www.mathnet.ru/eng/tm/v282/p114
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Abstract page: | 177 | Full-text PDF : | 46 | References: | 36 |
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