One-point asymptotics for half-flat ASEP

Abstract

We consider the asymmetric simple exclusion process (ASEP) with half-flat initial condition. We show that the one-point marginals of the ASEP height function are described by those of the ${\text{Airy}}_{2\to 1}$ process, introduced by Borodin–Ferrari–Sasamoto in (Comm. Pure Appl. Math. 61 (2008) 1603–1629). This result was conjectured by Ortmann–Quastel–Remenik (Ann. Appl. Probab. 26 (2016) 507–548), based on an informal asymptotic analysis of exact formulas for generating functions of the half-flat ASEP height function at one spatial point. Our present work provides a fully rigorous derivation and asymptotic analysis of the same generating functions, under certain parameter restrictions of the model.