# Probability Seminar

# Fall 2021

**Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom**

We usually end for questions at 3:20 PM.

ZOOM LINK. Valid only for online seminars.

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## September 16, 2021, in person: Hanbayek Lyu (UW-Madison)

**Scaling limit of soliton statistics of a multicolor box-ball system**

The box-ball systems (BBS) are integrable cellular automata whose long-time behavior is characterized by the soliton solutions, and have rich connections to other integrable systems such as Korteweg-de Veris equation. Probabilistic analysis of BBS is an emerging topic in the field of integrable probability, which often reveals novel connection between the rich integrable structure of BBS and probabilistic phenomena such as phase transition and invariant measures. In this talk, we give an overview on the recent development in scaling limit theory of multicolor BBS with random initial configurations. Our analysis uses various methods such as modified Greene-Kleitman invariants for BBS, circular exclusion processes, Kerov–Kirillov–Reshetikhin bijection, combinatorial R, and Thermodynamic Bethe Ansatz.