Scaling limits of solitons in the box-ball system

2024/11/22 by Stefano Olla, Olla, Stefano, Makiko Sasada +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #37B15(primary) #82C22 #82C23 (secondary) #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Waves and Solitons #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2411.14818

openalex publication_date 2024/11/22 · openalex created_date 2024/11/30 · openalex updated_date 2026/07/28

Abstract

We study the space-time scaling limits of solitons in the box-ball system with random initial distribution. In particular, we show that any recentered tagged soliton converges to a Brownian motion in the diffusive space-time scale, and also prove the large deviation principle for the tagged soliton under certain shift-ergodic invariant distributions, including Bernoulli product measures and two-sided Markov distributions. Furthermore, in the diffusive space-time scaling, we show that two tagged solitons converge to the same Brownian motion even if they are macroscopically far apart.

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