Date
February 14 (Fri) at 15:00 - 17:00, 2025 (JST) Tomorrow
Speaker
  • Ryosuke Sato (JSPS Postdoctoral Research Fellow, Faculty of Science and Engineering, Chuo University)
Language
English
Host
Kan Kitamura

A point process is a mathematical description of a particle system with random interactions, and it naturally appears in various areas of mathematical physics and mathematics, including statistical mechanics, random matrix theory, combinatorics, and representation theory. In particular, a random particle system with repulsive interactions is associated with a determinantal point process, in which the correlation of any number of particles is expressed in terms of the two-particle correlation via a determinant.

Furthermore, this determinantal structure enables an algebraic analysis using CAR algebras, which are operator algebras determined by canonical anti-commutation relations.

In the first half of the talk, we will review the relationship between determinantal point processes and operator algebras, with a focus on why operator algebras naturally lend themselves to analyses in probability theory and statistical mechanics. In the second half, based on recent work, we will examine the dynamic relationship between point processes and operator algebras, discussing how dynamics on CAR algebras give rise to stochastic processes on determinantal point processes.

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