Book ChapterDOI
Ultradiscrete Systems (Cellular Automata)
Tetsuji Tokihiro
- Vol. 644, pp 383-424
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The article was published on 2004-01-01. It has received 20 citations till now. The article focuses on the topics: Continuous automaton & Block cellular automaton.read more
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Dynamics of the box-ball system with random initial conditions via Pitman's transformation
TL;DR: In this paper, the authors studied the invariance of Bernoulli product measures with density strictly less than 1/2 and gave a soliton decomposition for invariant measures more generally.
Journal ArticleDOI
Three-level description of the domino cellular automaton
TL;DR: In this paper, a three-level description of cellular automata is presented, motivated by the approach of kinetic theory of gases, and a simple domino cellular automaton with avalanches is constructed.
Journal ArticleDOI
Multi-indexed Wilson and Askey-Wilson Polynomials
Satoru Odake,Ryu Sasaki +1 more
TL;DR: In this article, the authors presented the multi-indexed Wilson and Askey-Wilson polynomials with pure imaginary shifts in one dimension, in the framework of discrete quantum mechanics.
Journal ArticleDOI
Invariant measures for the box-ball system based on stationary Markov chains and periodic Gibbs measures
David A. Croydon,Makiko Sasada +1 more
TL;DR: In this article, Croydon et al. presented a series of invariant measures for the box-ball system with random initial conditions via Pitman's transformation, and also introduced a family of new ones for periodic configurations that are expressed in terms of Gibbs measures.
Journal ArticleDOI
Invariant measures for the box-ball system based on stationary Markov chains and periodic Gibbs measures
David A. Croydon,Makiko Sasada +1 more
TL;DR: In this paper, a survey of invariant measures for the box-ball system is presented, together with a family of new ones for periodic configurations that are expressed in terms of Gibbs measures.
References
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Journal ArticleDOI
Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
TL;DR: In this paper, the ground-state problem of spin-textonehalf{} fermions is reduced to a generalized Fredholm equation, in a generalized form, by using Bethe's hypothesis.
Journal ArticleDOI
Partition function of the eight vertex lattice model
TL;DR: In this paper, the partition function of the zero-field eight-vertices model on a square M by N lattice is calculated exactly in the limit of M, N large.
Journal ArticleDOI
Vibration of a Chain with Nonlinear Interaction
TL;DR: In this paper, the exact solutions to the equation of motion are aimed at using a transformation to obtain the Jacobian elliptic functions for a special type of interaction potential of the form \begin{aligned} \phi(r){=}\frac{a}{b}e^{-br}+ar+\text{const.