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- Title
Kernels of conditional determinantal measures and the Lyons-Peres completeness conjecture.
- Authors
Bufetov, Alexander I.; Yanqi Qiu; Shamov, Alexander
- Abstract
The main result of this paper, Theorem 1.4, establishes a conjecture of Lyons and Peres: for a determinantal point process governed by a self-adjoint reproducing kernel, the system of kernels sampled at the points of a random configuration is complete in the range of the kernel. A key step in the proof, Lemma 1.9, states that conditioning on the configuration in a subset preserves the determinantal property, and the main Lemma 1.10 is a new local property for kernels of conditional point processes. In Theorem 1.6 we prove the triviality of the tail -algebra for determinantal point processes governed by self-adjoint kernels.
- Subjects
SUBSET selection; POINT processes; HOLOMORPHIC functions; LEBESGUE measure; INTERPOLATION; RADON measures
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2021, Vol 23, Issue 5, p1477
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/1038