Scaling limits of solitons in the box-ball system

Stefano Olla; Makiko Sasada; Hayate Suda

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arXiv · 2411.14818

Scaling limits of solitons in the box-ball system

Stefano Olla·Makiko Sasada·Hayate Suda

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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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Stefano Olla, Makiko Sasada, Hayate Suda. 2024-11-22. Scaling limits of solitons in the box-ball system. https://arxiv.org/abs/2411.14818

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