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A note on the diffusivity of finite-range asymmetric exclusion processes on \(\mathbb Z\). (English) Zbl 1173.82341
Sidoravicius, Vladas (ed.) et al., In and out of equilibrium 2. Papers celebrating the 10th edition of the Brazilian school of probability (EBP), Rio de Janiero, Brazil, July 30 to August 4, 2006. Basel: Birkhäuser (ISBN 978-3-7643-8785-3/hbk). Progress in Probability 60, 543-549 (2008).
Summary: The diffusivity \(D(t)\) of finite-range asymmetric exclusion processes on \(\mathbb Z\) with non-zero drift is expected to be of order \(t^{1/3}\). Seppäläinen and Balázs recently proved this conjecture for the nearest neighbor case. We extend their results to general finite range exclusion by proving that the Laplace transform of the diffusivity is of the conjectured order. We also obtain a pointwise upper bound for \(D(t)\) of the correct order.
For the entire collection see [Zbl 1141.82002].

82C22 Interacting particle systems in time-dependent statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory