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

Fingerprint

Discrete Approximation
Point Process
Tail
approximation
analytic functions
Bergman Kernel
Zero Point
Gaussian Function
Friedrich Wilhelm Bessel
Thermodynamic Limit
Random Matrices
eigenvalues
theorems
Analytic function
Trivial
thermodynamics
Eigenvalue
Theorem

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Discrete Approximations of Determinantal Point Processes on Continuous Spaces : Tree Representations and Tail Triviality. / Osada, Hirofumi; Osada, Shota.

In: Journal of Statistical Physics, Vol. 170, No. 2, 01.01.2018, p. 421-435.

Research output: Contribution to journalArticle

@article{e66abac90a6446d3a53d47511718fb7b,
title = "Discrete Approximations of Determinantal Point Processes on Continuous Spaces: Tree Representations and Tail Triviality",
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.",
author = "Hirofumi Osada and Shota Osada",
year = "2018",
month = "1",
day = "1",
doi = "10.1007/s10955-017-1928-2",
language = "English",
volume = "170",
pages = "421--435",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "2",

}

TY - JOUR

T1 - Discrete Approximations of Determinantal Point Processes on Continuous Spaces

T2 - Tree Representations and Tail Triviality

AU - Osada, Hirofumi

AU - Osada, Shota

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85035115601&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85035115601&partnerID=8YFLogxK

U2 - 10.1007/s10955-017-1928-2

DO - 10.1007/s10955-017-1928-2

M3 - Article

AN - SCOPUS:85035115601

VL - 170

SP - 421

EP - 435

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 2

ER -