Cutoff and discrete Product Structure in ASEP

Abstract

We consider the asymmetric simple exclusion process (ASEP) on $\mathbb{Z}$ with an initial data such that in the large time particle density $\rho (\cdot )$ a discontinuity at the origin is created, where the value of $\rho$ jumps from zero to one, but $\rho (-\epsilon ),1-\rho (\epsilon )>0$ for any $\epsilon >0$. We consider the position of a particle $x_M$ macroscopically located at the discontinuity, and show that its limit law has a cutoff under $t^{1/2}$ scaling. Inside the discontinuity region, we show that a discrete product limit law arises, which bounds from above the limiting fluctuations of $x_M$ 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 Note: This preprint has been superseded by arXiv:1906.07711 and is no longer updated.

arXiv commentThis preprint has been superseded by arXiv:1906.07711 and is no longer updated

References in corpus (10)

• Asymptotics in ASEP with Step Initial Condition
• Fluctuation properties of the TASEP with periodic initial configuration
• Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Current Fluctuations of the Stationary ASEP and Six-Vertex Model
• Slow decorrelations in KPZ growth
• The ASEP and determinantal point processes
• A Pfaffian representation for flat ASEP
• Shock fluctuations in flat TASEP under critical scaling
• Finite GUE distribution with cut-off at a shock