Discrete Approximations of Determinantal Point Processes on Continuous Spaces: Tree Representations and Tail Triviality

研究成果: Contribution to journalArticle査読

8 被引用数 (Scopus)

抄録

We prove tail triviality of determinantal point processes μ on continuous spaces. Tail triviality has been proved for such processes only on discrete spaces, and hence we have generalized the result to continuous spaces. To do this, we construct tree representations, that is, discrete approximations of determinantal point processes enjoying a determinantal structure. There are many interesting examples of determinantal point processes on continuous spaces such as zero points of the hyperbolic Gaussian analytic function with Bergman kernel, and the thermodynamic limit of eigenvalues of Gaussian random matrices for Sine 2, Airy 2, Bessel 2, and Ginibre point processes. Our main theorem proves all these point processes are tail trivial.

本文言語英語
ページ(範囲)421-435
ページ数15
ジャーナルJournal of Statistical Physics
170
2
DOI
出版ステータス出版済み - 1 1 2018

All Science Journal Classification (ASJC) codes

  • 統計物理学および非線形物理学
  • 数理物理学

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