2018/12/31 by Peter Nejjar, Nejjar, Peter
Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1812.11939
openalex publication_date 2018/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the asymmetric simple exclusion process (ASEP) on ℤ with an initial data such that in the large time particle density ρ(⋅) a discontinuity at the origin is created, where the value of ρ jumps from zero to one, but ρ(-ε),1-ρ(ε) >0 for any ε>0. We consider the position of a particle xM macroscopically located at the discontinuity, and show that its limit law has a cutoff under t1/2 scaling. Inside the discontinuity region, we show that a discrete product limit law arises, which bounds from above the limiting fluctuations of xM in the general ASEP, and equals them in the totally ASEP. Note: This preprint has been superseded by arXiv:1906.07711 and is no longer updated.