Kernels of conditional determinantal measures and the proof of the Lyons-Peres Conjecture

Alexander I. Bufetov; Yanqi Qiu; Alexander Shamov

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arXiv · 1612.06751

Kernels of conditional determinantal measures and the proof of the Lyons-Peres Conjecture

Alexander I. Bufetov·Yanqi Qiu·Alexander Shamov

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Abstract

The main result of this paper, Theorem 1.5, establishes a conjecture of Lyons and Peres: for a determinantal point process governed by a reproducing kernel, the system of kernels sampled at the particles of a random configuration is complete in the range of the kernel. A key step in the proof, Lemma 1.11, states that conditioning on the configuration in a subset preserves the determinantal property, and the main Lemma 1.12 is a new local property for kernels of conditional point processes. In Theorem 1.7 we prove the triviality of the tail sigma-algebra for determinantal point processes governed by self-adjoint kernels.

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BibTeX RIS

Alexander I. Bufetov, Yanqi Qiu, Alexander Shamov. 2016-12-20. Kernels of conditional determinantal measures and the proof of the Lyons-Peres Conjecture. https://arxiv.org/abs/1612.06751

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