Pablo Ferrari is Researcher of the Consejo Nacional de Investigaciones Científicas y Técnicas, CONICET, in Argentina, and Emeritus Professor at the Universidad de Buenos Aires. He is Licenciado en Matemática at the same university, and Doutor em Estatística at the Universidade de São Paulo, Brazil; he joined their Department of Statistics, where he was a professor for many years. Pablo works in interacting particle systems, cellular automata, point processes and statistical mechanics models. Pablo was associate editor of the Annals of Probability, Probability Theory and Related Fields and a few other probability journals. He is a member of the Brazilian Academy of Sciences, the Academia de Ciencias Exactas, Físicas y Naturales and Academia Nacional de Ciencias, Argentina. He is an honored IMS Fellow and elected member of the ISI.

This Bernoulli–IMS Doob Lecture will be given at the 11th World Congress in Probability and Statistics, August 12–16, 2024, in Bochum, Germany: https://www.bernoulli-ims-worldcongress2024.org. Doob lectures are co-sponsored by the Bernoulli Society and IMS.

Soliton decomposition of the box-ball system and the Pitman transformation

The box-ball system is a one-dimensional, discrete time, transport cellular automaton introduced by Takahashi and Satsuma in 1990. Each box-ball configuration can be associated with a one-dimensional walk, and a dynamical step of the configuration is equivalent to the reflection of the excursions in the walk, an operation known as Pitman’s transformation. The evolution preserves pieces of the walk called solitons because they propagate conserving shape and speed, even after colliding with another such piece. By associating each soliton with the vector of its position and its height, one obtains a discrete (multi)set of points in the upper half plane, called the soliton decomposition of the walk. The position is measured in a “slot metric” determined by the walk for each soliton’s height. After one step of the dynamics, each point in the decomposition preserves its height, while its position is incremented by its height. In the continuous case, the walk is a continuous piecewise linear function; for the classic Markovian zig-zag random walk, the decomposition is a Poisson process. This approach is used to construct a large family of invariant measures for the dynamics, perform generalized hydrodynamic limits, and study limiting Gaussian fields. In this talk, I will survey the above results.