KPZ fixed point convergence of the ASEP and stochastic six-vertex models

2024/12/24 by Amol Aggarwal, Ivan Corwin, Aggarwal, Amol +3 · 2 citations
Computer Science · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2412.18117

openalex publication_date 2024/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider the stochastic six-vertex (S6V) model and asymmetric simple exclusion process (ASEP) under general initial conditions which are bounded below lines of arbitrary slope at ±∞. We show under Kardar-Parisi-Zhang (KPZ) scaling of time, space, and fluctuations that the height functions of these models converge to the KPZ fixed point. Previously, our results were known in the case of ASEP (for a particular direction in the rarefaction fan) via a comparison approach arXiv:2008.06584.

Cited by

• Limit profiles of ASEP
• Multipoint distributions of the KPZ fixed point with compactly supported initial conditions

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