Appears in collections : Random matrices and determinantal process / Matrices aléatoires. Processus déterminantaux, Exposés de recherche
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. Joint work with Alexander Bufetov and Yanqi Qiu.
By Claire David
By Dalia Terhesiu
