Slot Decomposition of the Box-Ball System - Part I

Explore the intricacies of the box-ball system in this 50-minute lecture by Pablo Ferrari, part of the Workshop on box-ball systems from integrable systems and probabilistic perspectives. Delve into the concept of "slot" used to describe ball configurations through their "soliton components" in this cellular automaton. Discover how solitons, conserved by the system's dynamics, travel at speeds proportional to their size and maintain shape even after collisions. Examine the hierarchical shift evolution of components and learn about the invariance of random initial ball configurations with translation-invariant and independent components. Investigate the soliton decomposition of an iid Bernoulli configuration and its relationship to geometric random variables. Uncover an alternative construction of the Harris correspondence between random walk excursions and trees using slot decomposition. This talk, based on joint works with Chi Nguyen, Leo Rolla, Minmin Wang, and Davide Gabrielli, offers a deep dive into the mathematical intricacies of the box-ball system.