2024/08/19 by Hindy Drillick, Drillick, Hindy, Levi Haunschmid-Sibitz +1 · 2 citations
Computer Science · Mathematics · #FOS: Mathematics #Graph Theory and Algorithms #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2408.10186
openalex publication_date 2024/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For the stochastic six-vertex model on the quadrant ℤ≥0×ℤ≥0 with step initial conditions and a single second-class particle at the origin, we show almost sure convergence of the speed of the second-class particle to a random limit. This allows us to define the stochastic six-vertex speed process, whose law we show to be ergodic and stationary for the dynamics of the multi-class stochastic six-vertex process. The proof follows the scheme developed in [ACG23] for ASEP and requires the development of precise bounds on the fluctuations of the height function of the stochastic six-vertex model around its limit shape using methods from integrable probability. As part of the proof, we also obtain a novel geometric stochastic domination result that states that a second-class particle to the right of any number of third-class particles will at any fixed time be overtaken by at most a geometric number of third-class particles.