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

Hirofumi Osada, Shota Osada

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)421-435
Number of pages15
JournalJournal of Statistical Physics
Volume170
Issue number2
DOIs
Publication statusPublished - Jan 1 2018

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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