Periodic TASEP with general initial conditions

• 成果类型: Article
• 署名作者: Baik, Jinho; Liu, Zhipeng
• 署名单位: University of Michigan System; University of Michigan; University of Kansas
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-020-01004-6
• 发表日期: 2021
• 页码: 1047-1144
• 关键词: polynuclear growth; spectral gap; fluctuations; asymptotics; formulas; borodin; MODEL; ring

摘要

We consider the one-dimensional totally asymmetric simple exclusion process with an arbitrary initial condition in a spatially periodic domain, and obtain explicit formulas for the multi-point distributions in the space-time plane. The formulas are given in terms of an integral involving a Fredholm determinant. We then evaluate the large-time, large-period limit in the relaxation time scale, which is the scale such that the system size starts to affect the height fluctuations. The limit is obtained assuming certain conditions on the initial condition, which we show that the step, flat, and step-flat initial conditions satisfy. Hence, we obtain the limit theorem for these three initial conditions in the periodic model, extending the previous work on the step initial condition. We also consider uniform random and uniform-step random initial conditions.