Wednesday, September 24, 2025 - 09:00 in Zoom Conference
Discrete $N$-particle systems at high temperature through Jack generating functions
A talk in the Bielefeld-Melbourne Seminar series by
Maciej Dołęga from Polish Academy of Sciences
| Abstract: |
We discuss random discrete $N$-particle systems with the deformation (inverse temperature) parameter $\theta$. We find necessary and sufficient conditions for the Law of Large Numbers as their size $N$ tends to infinity simultaneously with the inverse temperature going to zero. We apply the general framework to obtain the LLN for a large class of Markov chains of $N$ nonintersecting particles with interaction of log-gas type, and the LLN for the multiplication of Jack polynomials, 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 and continuous log-gas systems. If time permits, we will discuss a crystallization phenomenon observed in this regime and describe it in terms of the real-rootedness of certain special functions. Based on joint work with Cesar Cuenca.
Within the CRC this talk is associated to the project(s): B5, C6 |
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