月曜解析セミナー：Operator-algebraic approach to stochastic dynamics on point processes, 佐藤 僚亮 氏

Time：16:30-18:00

Place：理学部3号館3-204室

Organizer：小林 政晴、洞 彰人、長谷部 高広、浜向 直、佐藤 僚亮

Speaker：佐藤 僚亮 氏 (北海道大学)

Title：Operator-algebraic approach to stochastic dynamics on point processes

Abstract：In this talk, we will study stochastic dynamics on point processes from the perspective of operator algebra theory. A point process is a random point configuration in a given space, and this concept naturally appears in various fields of mathematics and mathematical physics, such as random matrix theory, representation theory, combinatorics, and statistical mechanics. From the viewpoint of operator algebras, (determinantal) point processes are intimately related to (quasi-free) states on CAR algebras, which are generated by Fermionic creation and annihilation operators. The purpose of this talk is to present recent progress on the dynamical relationship between stochastic processes on point configurations and CAR algebras. We will show that the framework based on KMS states on CAR algebras, which characterize thermal equilibrium states in quantum statistical mechanics, is applicable to constructing and analyzing stochastic processes on point configurations.