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We prove the Bernoulli property for determinantal point processes on $\mathbb{R}^d $ with translation-invariant kernels. For the determinantal pointprocesses on $ \mathbb{Z}^d $ with translation-invariant kernels, the Bernoulliproperty was proved by Lyons and Steif and Shirai and Takahashi. As itscontinuum version, we prove an isomorphism between the translation-invariantdeterminantal point processes on $ \mathbb{R}^d $ with translation-invariantkernels and homogeneous Poisson point processes. For this purpose, we alsoprove the Bernoulli property for the tree representations of the determinantalpoint processes.

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