We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Random walk in mixed random environment without uniform ellipticity.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Download PDF
Publisher Web site:
Publisher statement:The final publication is available at Springer via
Date accepted:No date available
Date deposited:20 December 2013
Date of first online publication:2013
Date first made open access:No date available

Save or Share this output

Look up in GoogleScholar