Scaling limits of solitons in the box-ball system
Probability
2025-05-07 v2
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.
Cite
@article{arxiv.2411.14818,
title = {Scaling limits of solitons in the box-ball system},
author = {Stefano Olla and Makiko Sasada and Hayate Suda},
journal= {arXiv preprint arXiv:2411.14818},
year = {2025}
}
Comments
81 pages, 11 figures. Some technical modifications were done to clarify the proofs