SHOCK FLUCTUATIONS IN TASEP UNDER A VARIETY OF TIME SCALINGS

• 成果类型: Article
• 署名作者: Bufetov, Alexey; Ferrari, Patrik L.
• 署名单位: University of Bonn
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1769
• 发表日期: 2022
• 页码: 3614-3644
• 关键词: phase-transition; limit law; particle; percolation

摘要

We consider the totally asymmetric simple exclusion process (TASEP) with two different initial conditions with shock discontinuities formed by blocks of fully packed particles. Initially a second class particle is at the left of a shock discontinuity. Using multicolored TASEP we derive exact formulas for the distribution of the second class particle and colored height functions. These are given in terms of the height function at different positions of a single TASEP configuration. We study the limiting distributions of second class particles (and colored height functions). The result depends on how the width blocks of particles scale with the observation time; we study a variety of such scalings.