Transport properties and ageing for the averaged Lévy-Lorentz gas

Abstract

We consider a persistent random walk on an inhomogeneous environment where the reflection probability depends only on the distance from the origin. Such an environment is the result of an average over all realizations of disorder of a Lévy-Lorentz (LL) gas. Here we show that this averaged Lévy-Lorentz gas yields nontrivial results even when the related LL gas is trivial. In particular, we investigate its long time transport properties such as the mean square displacement and the statistics of records, as well as the occurrence of ageing phenomena.

arXiv comment16 pages, 6 figures

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Cited by in corpus (8)

• Statistics of occupation time and connection to local properties of non-homogeneous random walks
• Exploring the Gillis model: a discrete approach to diffusion in logarithmic potentials
• Record Ages of Scale Invariant non-Markovian Random Walks
• Extreme value statistics of positive recurrent centrally biased random walks
• Large fluctuations and transport properties of the Lévy-Lorentz gas
• Ladder costs for random walks in Lévy random media
• Limit theorems for Lévy flights on a 1D Lévy random medium
• Records and occupation time statistics for area-preserving maps