Corpus ID: 119131097

Dynamics of the box-ball system with random initial conditions via Pitman's transformation

@article{Croydon2018DynamicsOT,
  title={Dynamics of the box-ball system with random initial conditions via Pitman's transformation},
  author={David A. Croydon and Tsuyoshi Kato and Makiko Sasada and Satoshi Tsujimoto},
  journal={arXiv: Probability},
  year={2018}
}
The box-ball system (BBS), introduced by Takahashi and Satsuma in 1990, is a cellular automaton that exhibits solitonic behaviour. In this article, we study the BBS when started from a random two-sided infinite particle configuration. For such a model, Ferrari et al.\ recently showed the invariance in distribution of Bernoulli product measures with density strictly less than $\frac{1}{2}$, and gave a soliton decomposition for invariant measures more generally. We study the BBS dynamics using… Expand

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