Quasi-Geodesics in Integrable and Non-Integrable Exclusion Processes

Abstract

Backwards geodesics for TASEP were introduced in [30]. We consider flat initial conditions and show that under proper scaling the end-point of the geodesic converges to maximizer argument of the \(\hbox {Airy}_2\) process minus a parabola. We generalize its definition to generic non-integrable models including ASEP and speed changed ASEP (call it quasi-geodesics). We numerically verify that its end-point is universal, where the scaling coefficients are analytically computed through the KPZ scaling theory.