Hryniv, Ostap and Menshikov, Mikhail V. and Wade, Andrew R. (2013) 'Random walk in mixed random environment without uniform ellipticity.', Proceedings of the Steklov Institute of Mathematics., 282 (1). pp. 106-123.
We study a random walk in random environment on 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.
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||http://dx.doi.org/10.1134/S0081543813060102|
|Publisher statement:||The final publication is available at Springer via http://dx.doi.org/10.1134/S0081543813060102.|
|Date accepted:||No date available|
|Date deposited:||20 December 2013|
|Date of first online publication:||2013|
|Date first made open access:||No date available|
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