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Symmetric Functions & Probability Theory Seminar

Discrete $N$-particle ensembles at high temperature through Jack symmetric functions

Cesar Cuenca (Ohio State)

Location:  Hill 705
Date & time: Wednesday, 12 November 2025 at 10:45PM - 11:45PM

I will speak about random discrete N-particle systems with the inverse temperature parameter theta. We find necessary and sufficient conditions for the Law of Large Numbers as the size N of the system tends to infinity simultaneously with the inverse temperature going to zero. We obtain the LLN for multiparameter families of Markov chains of N nonintersecting particles and the LLN for the multiplication of Jack symmetric functions, as the inverse temperature tends to zero. We express the answer in terms of novel one-parameter deformations of cumulants and discuss their relation to (quantized) free probability. Finally, we discuss a crystallization phenomenon and describe it in terms of the countable real roots of certain special functions. The talk is based on joint work with Maciej Dolega.

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