The Chaotic Properties of the Point Processes
25 September – 6 October, 2017

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

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.

Participants :
Alexander Bufetov (CNRS Aix-Marseille Université)
Pierre Lazag (Aix-Marseille Université)
Ivan Losev (Massachusetts Institute of Technology)
Sasha Sodin (QMUL and TAU)
Marco Stevens (KU Leuven)
Alexander Tarasov (Higher School of Economics, ​ Moscow)
Dmitry Zubov (Higher School of Economics, Moscow)

Spectral properties of parabolic flows
3 – 12 October, 2018

Organizing Committee
Alexander Bufetov (CNRS, Aix-Marseille Université)

This working group will continue work on spectral properties of parabolic flows. The global objective is to give a quantitative description of the spectral measure. The first quantitative estimates for the spectral measures were obtained by the authors in a series of papers starting in 2012 through 2018. We have however only so far been able to obtain upper bounds for the spectral measure, and the aim of this workshop will be to give lower bounds as well. 

​Adrien Boulanger (Université Pierre et Marie Curie)
Pascal Hubert (Aix-Marseille Université)
Pierre Lazag(Aix-Marseille Université)
Juan Marshall (Aix-Marseille Université)
Boris Solomyak (​University of Bar-Ilan)

Determinantal Markov Processes (WK N° 2273)
28 January – 1 February, 2019

Organizing Committee
Alexander Bufetov (Aix-Marseille Université)
Romain Teychene (Aix-Marseille Université)

For several key examples of determinantal processes emerging in random matrix theory  it is possible to construct their time-dependent determinantal  extension. For instance, the sine-process is extended to  the dynamical sine-process, the scaling limit of the Dyson Brownian motion, a time-dependent determinantal Markov process.  It remains mysterious in what generality such determinantal Markov extensions exist, and the working group is devoted to the study of this problem.

Participants :
Adrien Boulanger (Université Paris 6)

Vladimir Fomichov (Higher School of Economics)
Pascal Hubert (Aix-Marseille Université)

Pierre Lazag (Aix-Marseille Université)
Juan Marshall (Aix-Marseille Université)

Dynamics of punctual processes ((WK N° 2361)
Dynamique des processus ponctuels
15 – 31 January, 2020

Organizing Committee
Alexander Bufetov (Aix-Marseille Université)

Les processus ponctuels déterminantaux ont des propriétés dynamiques a la frontière entre l’ordre et le chaos — par exemple, ils satisfont a la fois au théorèmes de la limite centrale et a la propriété de rigidité de Ghosh et Peres. La rencontre sera dédiée aux propriétés chaotiques des processus ponctuels, portant une attention spéciale sur les cas déterminantal et pfaffien.

Participants :
Sergey Berezin (Aix-Marseille Université)
Adrien Boulanger (Université Paris 6)

Pierre Lazag (Aix-Marseille Université)
Yiting Li (Aix Marseille Université)

Juan Marshall (Aix-Marseille Université)
Ilia Smilga (
Université Paris-Sud)
Yanqi Qiu (Chinese Academy of Sciences, Beijing)


These projects has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement N°647113)