{BBS} invariant measures with independent soliton components.

PABLO A. FERRARI; DAVIDE GABRIELLI

ELECTRONIC JOURNAL OF PROBABILITY

UNIV WASHINGTON

Lugar: Seatle; Año: 2020 vol. 25 p. 1 - 26

1083-6489

We review combinatorial properties of solitons of the Box-Ball system introduced by Takahashi and Satsuma. Starting with several definitions of the system, we describe ways to identify solitons and review a proof of the conservation of the solitons under the dynamics. Ferrari, Nguyen, Rolla and Wang proposed a soliton decomposition of an excursion over the current minima of the walk representative of a ball configuration. Building on this approach, we propose a new soliton decomposition which is equivalent to the classical branch decomposition of the tree associated to the excursion. When the ball occupation numbers are independent Bernoulli variables of parameter λ