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$$t^{1/3}$$ superdiffusivity of finite-range asymmetric exclusion processes on $${\mathbb{Z}}$$. (English) Zbl 1127.60091
The authors consider finite-range asymmetric exclusion processes (AEP) on the integer lattice $${\mathbb Z}$$ with non-zero drift. For such processes they prove that the diffusivity $$D (t)$$ satisfies $$D (t) \geq Ct ^{1/3}$$. For the particular case of a totally asymmetric simple exclusion process (TASEP) the estimate confirms previous results of P. L. Ferrari and H. Spohn [Commun. Math. Phys. 265, No. 1, 1–44, erratum 45–46 (2006; Zbl 1118.82032)] obtained by means of a different technique, thus partially confirming the predicted universality of the abovementioned results.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82C22 Interacting particle systems in time-dependent statistical mechanics 82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
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