Dynamical relationship between CAR algebras and determinantal point processes: point processes at finite temperature and stochastically positive KMS systems

Ryosuke Sato

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arXiv · 2504.12935

Dynamical relationship between CAR algebras and determinantal point processes: point processes at finite temperature and stochastically positive KMS systems

Ryosuke Sato

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Abstract

The aim of this paper is threefold. Firstly, we develop the author's previous work on the dynamical relationship between determinantal point processes and CAR algebras. Secondly, we present a novel application of the theory of stochastic processes associated with KMS states for CAR algebras and their quasi-free states. Lastly, we propose a unified theory of algebraic constructions and analysis of stationary processes on point configuration spaces with respect to determinantal point processes. As a byproduct, we establish an algebraic derivation of a determinantal formula for space-time correlations of stochastic processes, and we analyze several limiting behaviors of these processes.

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BibTeX RIS

Ryosuke Sato. 2025-04-17. Dynamical relationship between CAR algebras and determinantal point processes: point processes at finite temperature and stochastically positive KMS systems. https://arxiv.org/abs/2504.12935

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