Spectral Analysis of Transition Operators, Automata Groups and Translation in BBS

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• 作者：Tsuyoshi Kato ; Satoshi Tsujimoto ; Andrzej Zuk
• 刊名：Communications in Mathematical Physics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：350
• 期：1
• 页码：205-229
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Complex Systems; Classical and Quantum Gravitation, Relativity Theory;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0916
• 卷排序：350

文摘

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.