CURRENT FLUCTUATIONS OF THE STATIONARY ASEP AND SIX-VERTEX MODEL

摘要

Our results in this article are twofold. First, we consider current fluctuations of the stationary asymmetric simple exclusion process (ASEP), run for some long time T, and show that they are of order T-1/3 along a characteristic line. Upon scaling by T-1/3, we establish that these fluctuations converge to the long-time height fluctuations of the stationary Kardar-Parisi-Zhang (KPZ) equation, that is, to the Baik-Rains distribution. This result has long been predicted under the context of KPZ universality and in particular extends upon a number of results in the field, including the work of Ferrari and Spohn from 2005 (when they established the same result for the TASEP) and the work of Balazs and Seppalainen from 2010 (when they established the T-1/3 scaling for the general ASEP).