Quasi-geodesics in integrable and non-integrable exclusion processes

TL;DR

This paper extends the concept of backwards geodesics from TASEP to more general exclusion processes, demonstrating their universal behavior and analytical scaling properties through numerical verification.

Contribution

It generalizes the definition of quasi-geodesics to non-integrable models like ASEP and verifies their universal end-point distribution numerically.

Findings

End-point converges to the maximizer of Airy$_2$ process minus parabola.

Universal scaling coefficients are analytically derived.

Numerical results support universality across models.

Abstract

Backwards geodesics for TASEP were introduced in [Fer18]. We consider flat initial conditions and show that under proper scaling its end-point converges to maximizer argument of the 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.