Collection Random matrices and determinantal process / Matrices aléatoires. Processus déterminantaux

Organisateur(s) Bufetov, Alexander ; Chhaibi, Reda ; Grava, Tamara ; Kuijlaars, Arno ; Krasovsky, Igor ; Nikitin, Pavel ; Savin, Dmitry

Date(s) 27/02/2017 - 03/03/2017

URL associée http://conferences.cirm-math.fr/1715.html

3 4

Conditioned determinantal processes are determinantal

De Alexander Shamov

Apparaît également dans la collection : 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.

Informations sur la vidéo

Date de captation 27/02/2017
Date de publication 10/03/2017
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19134203
Citer cette vidéo Shamov, Alexander (27/02/2017). Conditioned determinantal processes are determinantal. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19134203
URL https://dx.doi.org/10.24350/CIRM.V.19134203