22 citations · 143 across the 51 of their papers we have counts for
4 papers · 1 filter
Duality between box-ball systems of finite box and/or carrier capacity
David A. Croydon, Makiko Sasada
We construct the dynamics of the box-ball system with box capacity and carrier capacity , which we abbreviate to BBS(,), in the case of infinite initial configurations…
Invariant measures for the box-ball system based on stationary Markov chains and periodic Gibbs measures
David A. Croydon, Makiko Sasada
The box-ball system (BBS) is a simple model of soliton interaction introduced by Takahashi and Satsuma in the 1990s. Recent work of the authors, together with Tsuyoshi Kato and Sat…
Dynamics of the ultra-discrete Toda lattice via Pitman's transformation
David A. Croydon, Makiko Sasada, Satoshi Tsujimoto
By encoding configurations of the ultra-discrete Toda lattice by piecewise linear paths whose gradient alternates between and , we show that the dynamics of the system can…
Biased random walk on the trace of biased random walk on the trace of...
David Croydon, Mark Holmes
We study the behaviour of a sequence of biased random walks X(i), i>=0 on a sequence of random graphs, where the initial graph is Zd and otherwise the graph for the i-th walk is th…