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We perform simulations for one dimensional continuous-time random walks intwo dynamic random environments with fast (independent spin-flips) and slow(simple symmetric exclusion) decay of space-time correlations, respectively. Wefocus on the asymptotic speeds and the scaling limits of such random walks. Weobserve different behaviors depending on the dynamics of the underlying randomenvironment and the ratio between the jump rate of the random walk and the oneof the environment. We compare our data with well known results for staticrandom environment. We observe that the non-diffusive regime known so far onlyfor the static case can occur in the dynamic setup too. Such anomalousfluctuations give rise to a new phase diagram. Further we discuss possibleconsequences for more general static and dynamic random environments.

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