Multi angle Conditioned determinantal processes are determinantal
Auteurs : Shamov, Alexander (Auteur de la Conférence)
CIRM (Editeur )
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Résumé : A determinantal point process governed by a Hermitian contraction kernel $K$ on a measure space $E$ remains determinantal when conditioned on its configuration on a subset $B \subset E$. Moreover, the conditional kernel can be chosen canonically in a way that is "local" in a non-commutative sense, i.e. invariant under "restriction" to closed subspaces $L^2(B) \subset P \subset L^2(E)$. Using the properties of the canonical conditional kernel we establish a conjecture of Lyons and Peres: if $K$ is a projection then almost surely all functions in its image can be recovered by sampling at the points of the process.Codes MSC :
Joint work with Alexander Bufetov and Yanqi Qiu.
60C05 - Combinatorial probability
60G55 - Point processes