Separation properties of a hybrid point process with determinantal radii and uniform arguments
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917183369510912 |
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| author | Lamberti, Giuseppe Massaneda, Xavier |
| author_facet | Lamberti, Giuseppe Massaneda, Xavier |
| contents | We recently characterized the separated determinantal point processes $Λ_ϕ$ associated with Fock spaces $\mathcal F_ϕ$ in the plane with doubling weight $ϕ$. We also showed that, as expected, a more restrictive condition is required to characterize the separated Poisson processes with the same first intensities as $Λ_ϕ$. To gain further insight into this different behavior, we center our attention to radial weights $ϕ(z)$ and introduce a hybrid process $Λ_ϕ^M=\{r_k e^{iθ_k}\}_{k=1}^\infty$, where the moduli $r_k$ are taken from $Λ_ϕ$, while the arguments $θ_k$ are chosen independently and uniformly in $[0,2π)$. Our main result is that $Λ_ϕ^M$ is almost surely separated if and only if its first intensity satisfies the same condition as in the Poisson case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01474 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Separation properties of a hybrid point process with determinantal radii and uniform arguments Lamberti, Giuseppe Massaneda, Xavier Complex Variables Functional Analysis Probability We recently characterized the separated determinantal point processes $Λ_ϕ$ associated with Fock spaces $\mathcal F_ϕ$ in the plane with doubling weight $ϕ$. We also showed that, as expected, a more restrictive condition is required to characterize the separated Poisson processes with the same first intensities as $Λ_ϕ$. To gain further insight into this different behavior, we center our attention to radial weights $ϕ(z)$ and introduce a hybrid process $Λ_ϕ^M=\{r_k e^{iθ_k}\}_{k=1}^\infty$, where the moduli $r_k$ are taken from $Λ_ϕ$, while the arguments $θ_k$ are chosen independently and uniformly in $[0,2π)$. Our main result is that $Λ_ϕ^M$ is almost surely separated if and only if its first intensity satisfies the same condition as in the Poisson case. |
| title | Separation properties of a hybrid point process with determinantal radii and uniform arguments |
| topic | Complex Variables Functional Analysis Probability |
| url | https://arxiv.org/abs/2601.01474 |