PETIT GROUPE DE TRAVAIL

Les propriétés chaotiques des processus ponctuels
25 septembre – 6 novembre 2017

Several important results in the theory of determinantal point processes were established during the past years. First of all, recall that a determinantal process is rigid if for any ball the number of points inside this ball is almost surely determined by the configuration outside  the ball. The proof of the rigidity for a list of determinantal point processes leads naturally to the investigation of the corresponding conditional measures, that were explicitly described by A.Bufetov for a large class of processes. The next natural question is to consider the limit when the size of the ball tends to infinity, it was done in a recent paper of A.Kujillars and E. Mina-Diaz.
Second, we have a recent proof of the functional CLT for the sine process by A.Bufetov and A.Dymov. Then, we have a partial proof of the uniqueness of the symmetric kernel of the process by M.Stevens. We plan to discuss the details of this fascinating developments and the methods of the proofs of the corresponding statements in Pfaffian case.
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement N°647113)
Comité d’organisation

Alexander Bufetov (Aix-Marseille Université)
Pavel Nikitin 
(Steklov Institute, St-Petersburg)