Isomorphisms between determinantal point processes with translation-invariant kernels and Poisson point processes

Shota Osada

Research output: Contribution to journalArticlepeer-review

Abstract

We prove the Bernoulli property for determinantal point processes on with translation-invariant kernels. For the determinantal point processes on with translation-invariant kernels, the Bernoulli property was proved by Lyons and Steif [Stationary determinantal processes: phase multiplicity, bernoullicity, and domination. Duke Math. J. 120 (2003), 515-575] and Shirai and Takahashi [Random point fields associated with certain Fredholm determinants II: fermion shifts and their ergodic properties. Ann. Probab. 31 (2003), 1533-1564]. We prove its continuum version. For this purpose, we also prove the Bernoulli property for the tree representations of the determinantal point processes.

Original languageEnglish
Pages (from-to)3807-3820
Number of pages14
JournalErgodic Theory and Dynamical Systems
Volume41
Issue number12
DOIs
Publication statusPublished - Dec 4 2021

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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