A Probabilistic View of the Box-ball System and other Discrete Integrable Systems

The box-ball system (BBS) was introduced by Takahashi and Satsuma as a simple discrete
model in which solitons (i.e. solitary waves) could be observed, and it has since been shown that it can be derived from the classical Korteweg-de-Vries equation, which describes waves in shallow water by a proper discretization. The last few years have seen a growing interest in the study of the BBS and related discrete integrable systems started from random initial conditions. Particular aims include characterizing measures that are invariant for the dynamics, exploring the soliton decompositions of random configurations, and establishing (generalized) hydrodynamic limits. In this talk, I will explain some recent progress in this direction.