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Fluctuations of TASEP on a Ring in Relaxation Time Scale
Author(s) -
Baik Jinho,
Liu Zhipeng
Publication year - 2018
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21702
Subject(s) - asymmetric simple exclusion process , mathematics , ring (chemistry) , ansatz , crossover , relaxation (psychology) , statistical physics , scale (ratio) , infinity , bethe ansatz , mathematical analysis , mathematical physics , physics , quantum mechanics , statistics , psychology , social psychology , integrable system , chemistry , organic chemistry , artificial intelligence , computer science
We consider the totally asymmetric simple exclusion process on a ring with flat and step initial conditions. We assume that the size of the ring and the number of particles tend to infinity proportionally and evaluate the fluctuations of tagged particles and currents. The crossover from the KPZ dynamics to the equilibrium dynamics occurs when the time is proportional to the 3/2 power of the ring size. We compute the limiting distributions in this relaxation time scale. The analysis is based on an explicit formula of the finite‐time one‐point distribution obtained from the coordinate Bethe ansatz method. © 2017 Wiley Periodicals, Inc.