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

2019/09/15 by Shota Osada, Osada, Shota
Mathematics · #Advanced Combinatorial Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1909.06973

openalex publication_date 2019/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the Bernoulli property for determinantal point processes on \n\ℝ^d with translation-invariant kernels. For the determinantal point\nprocesses on \ℤ^d with translation-invariant kernels, the Bernoulli\nproperty was proved by Lyons and Steif and Shirai and Takahashi. As its\ncontinuum version, we prove an isomorphism between the translation-invariant\ndeterminantal point processes on \ℝ^d with translation-invariant\nkernels and homogeneous Poisson point processes. For this purpose, we also\nprove the Bernoulli property for the tree representations of the determinantal\npoint processes.\n

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