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MR2318311 60K35 (60J25 82B41 82C22)
Quastel, Jeremy; Valko, Benedek $t^{1/3}$ Superdiffusivity of finite-range asymmetric exclusion processes on $\Bbb Z$. Comm. Math. Phys. 273 (2007), no. 2, 379–394.
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