Quasi-geodesics in integrable and non-integrable exclusion processes

2024/12/16 by Patrik L. Ferrari, Min Liu, Ferrari, Patrik L. +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2412.11626

openalex publication_date 2024/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Airy₂ 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.

Related

• Non-existence of three non-coalescing infinite geodesics with the same direction in the directed landscape
• About Hydrodynamic Limit of Some Exclusion Processes via Functional Integration
• Infinite order phase transition in the slow bond TASEP
• Stochastic Dynamics of Discrete Curves and Exclusion Processes. Part 1: Hydrodynamic Limit of the ASEP System
• On the KPZ scaling and the KPZ fixed point for TASEP