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

Part of: Ergodic theory Stochastic processes

Published online by Cambridge University Press:  04 December 2020

SHOTA OSADA Open the ORCID record for SHOTA OSADA [Opens in a new window]
SHOTA OSADA*
Affiliation:
Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
*
e-mail: s-osada@math.kyushu-u.ac.jp
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Abstract

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We prove the Bernoulli property for determinantal point processes on $ \mathbb{R}^d $ with translation-invariant kernels. For the determinantal point processes on $ \mathbb{Z}^d $ 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.

Keywords

Bernoulli propertydeterminantal point processestree representations

MSC classification

Primary: 37A50: Relations with probability theory and stochastic processes
Secondary: 60G55: Point processes

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 12 , December 2021 , pp. 3807 - 3820
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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