CONICET | Buscador de Institutos y Recursos Humanos

The Box-Ball System (BBS) is a one-dimensional cellular automaton in {0,1}ℤ introduced by Takahashi and Satsuma, who also identified conserved sequences called solitons. Integers are called boxes and a ball configuration indicates the sites occupied by balls. For each integer k≥1, a k-soliton consists of k boxes occupied by balls and k empty boxes. Ferrari, Nguyen, Rolla and Wang define the k-slots of a configuration as the places where k-solitons can be appended. Labeling the k-slots with integer numbers, they define the k-component of the configuration as the element of ℤ≥0 giving the number of k-solitons appended to each k-slot. They also show that shift-invariant distribution with independent soliton components are invariant for the automaton. We show that for each λ∈[0,1/2) the product measure on ball configurations with parameter λ has independent soliton components and that its k-component is a product measure of geometric random variables with parameter 1−qk(λ), an explicit function of λ. The construction is used to describe a large family of invariant measures with independent components, including Ising like measures.