Spectral analysis of transition operators, Automata groups and translation in BBS
Spectral Theory
2016-05-04 v2 Group Theory
Exactly Solvable and Integrable Systems
Abstract
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.
Cite
@article{arxiv.1406.5557,
title = {Spectral analysis of transition operators, Automata groups and translation in BBS},
author = {Tsuyoshi Kato and Satoshi Tsujimoto and Andrzej Zuk},
journal= {arXiv preprint arXiv:1406.5557},
year = {2016}
}