Continuity and Anomalous Fluctuations in Random Walks in Dynamic Random Environments: Numerics, Phase Diagrams and Conjectures

We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on the asymptotic speeds and the scaling limits of such random...

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Bibliographic Details
Published in:Journal of statistical physics 2012-07, Vol.147 (6), p.1041-1067
Main Authors: Avena, L., Thomann, P.
Format: Article
Language:English
Subjects:
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary:We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on the asymptotic speeds and the scaling limits of such random walks. We observe different behaviors depending on the dynamics of the underlying random environment and the ratio between the jump rate of the random walk and the one of the environment. We compare our data with well known results for static random environment. We observe that the non-diffusive regime known so far only for the static case can occur in the dynamical setup too. Such anomalous fluctuations give rise to a new phase diagram. Further we discuss possible consequences for more general static and dynamic random environments.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-012-0502-1