Abstract
We give the automata that describe time evolution rules of the box-ball system with a carrier. It can be shown by use of tropical geometry that such systems are ultradiscrete analogues of KdV equation. We discuss their relation with the lamplighter group generated by an automaton. We present spectral analysis of the stochastic matrices induced by these automata and verify their spectral coincidence.
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Communicated by A. Borodin
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Kato, T., Tsujimoto, S. & Zuk, A. Spectral Analysis of Transition Operators, Automata Groups and Translation in BBS. Commun. Math. Phys. 350, 205–229 (2017). https://doi.org/10.1007/s00220-016-2702-z
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DOI: https://doi.org/10.1007/s00220-016-2702-z