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Isomorphisms between determinantal point processes with translation-invariant kernels and Poisson point processes
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 41 / Issue 12 / December 2021
- Published online by Cambridge University Press:
- 04 December 2020, pp. 3807-3820
- Print publication:
- December 2021
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- Article
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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.
