Integrability of Box-Ball Systems and Randomized Box-Ball Systems - Part II

Explore the intricacies of box-ball systems and their randomized counterparts in this comprehensive lecture. Delve into the integrability of box-ball systems, examining their emergence from classical integrable systems through ultradiscretization and as quantum integrable systems at q = 0. Survey the synthesis of this dual origin of integrability, focusing on combinatorial Bethe ansatz and crystals theory in quantum groups. Discover how these concepts relate to soliton theory, including rigged configurations as action-angle variables, KKR bijection as inverse scattering transformation, and more. Learn about the recently formulated complete box ball system in higher rank with a completely diagonal S matrix. Investigate randomized box-ball systems, exploring analytical and simulation results obtained through TBA and GHD. Examine topics such as exact solutions of TBA equations, limit shapes of conserved Young diagrams, density plateaux from domain wall initial conditions, and long-time behavior of generalized current correlations. Gain insights into the large deviation function for ball currents and other advanced concepts in this 48-minute lecture presented at the Workshop on box-ball systems from integrable systems and probabilistic perspectives.