Spectral analysis of transition operators, Automata groups and   translation in BBS
  We give the automata which describe time evolution rules of the box-ball system (BBS) with a carrier. It can be shown by use of tropical geometry, 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. 
Tsuyoshi Kato, Satoshi Tsujimoto, Andrzej Zuk
math.SP math.GR nlin.SI