Continuity and anomalous fluctuations in random walks in dynamic random environments: numerics, phase diagrams and conjectures

Details Continuity and anomalous fluctuations in random walks in dynamic random environments: numerics, phase diagrams and conjectures Continuity and anomalous fluctuations in random walks in dynamic random environments: numerics, phase diagrams and conjectures

2012-01-13

arxiv.org/abs/1201.2890v1

Mathematics

Probability

31 pages, 22 figures

Scientific paper

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 dynamic setup too. Such anomalous fluctuations emerge in a new phase diagram. Further we discuss possible consequences for general static and dynamic random environments.

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