Stochastic Box-Ball System - Convergence to Brownian Motion

Explore the stochastic version of the box-ball system in this 40-minute lecture presented by David Keating from the University of Wisconsin-Madison at IPAM's Vertex Models workshop. Delve into the deterministic discrete-time dynamical system introduced by Takahashi and Satsuma, where boxes at each natural number can hold a single ball or be empty. Discover how the introduction of a failure probability ϵ transforms the system into a stochastic model. Examine the focus on inter-distance configurations rather than individual ball positions, and learn about the main result showing convergence to semi-martingale reflecting Brownian motion after suitable rescaling. Gain insights into this fascinating topic at the intersection of pure and applied mathematics.