Random Matrices and Determinantal Process
February 27 – March 3, 2017

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°

The past decade has seen rapid developments in various areas of mathematics related to the random matrix theory.
– First, studies of the properties of Wigner and other ensembles of random matrices using methods of the probability theory.
– Second, studies of the properties of orthogonal polynomials, Toeplitz determinants, and Fredholm determinants with universal kernels, by methods of asymptotic analysis with implications for the invariant ensembles of random matrices.
– Third, studies of random particle systems appearing in the group representation theory.
– Fourth, studies of random walks.
– Fifth, applications of random matrices in statistical physics and number theory.

These subjects will form the scope of the week devoted to random matrices. They employ a variety of different methods but deal with not dissimilar objects, therefore we believe that a useful exchange of ideas and creation of new exciting mathematics in the intersection between these subjects is assured.

Scientific Committee & Organizing Committee

Alexander Bufetov (Aix-Marseille Université)
Reda Chhaibi (Université Paul Sabatier Toulouse)
Tamara Grava (SISSA Trieste & University of Bristol)
Arno Kuijlaars (KU Leuven)
Igor Krasovsky (Imperial College London)
Pavel Nikitin (Aix-Marseille Université)
Dmitry Savin (Brunel University London)

« We the organizers of this conference affirm that scientific events must be open to everyone, regardless of race, sex, religion, national origin, sexual orientation, gender identity, disability, age, pregnancy, immigration status, or any other aspect of identity. We believe that such events must be supportive, inclusive, and safe environments for all participants. We believe that all participants are to be treated with dignity and respect. Discrimination and harassment cannot be tolerated. We are committed to ensuring that the conference « Random Matrices and Determinantal Process » follows these principles. For more information on the Statement of Inclusiveness, see this dedicated web page [1]. »

Universality in products of two coupled random matrices: Finite rank perturbations 

Fluctuations of the free energy of spherical Sherrington-Kirkpatrick model 

Complexity of high dimensional random landscapes: a phase transition

The Kontsevich matrix integral and Painlevé hierarchy; rigorous asymptotics and universality at the soft edges of the spectrum in random matrix theory   (slides)

Random Matrix Theory and Representation Theory​

Random Matrices and Exact Solution of the Six-Vertex Model with Half-Turn Boundary Conditions 

Near-extreme eigenvalues of random matrices and systems of coupled Painlevé II equations   (slides)

Fluctuations of linear statistics for biorthogonal ensembles   (slides)

A functional limit theorem for the sine-process 

Exponential number of equilibria and depinning threshold for a directed polymer in a random potential 

Height fluctuations through Schur generating functions 

Determinantal processes in higher dimension and Monte Carlo

The Airy point process in the two-periodic Aztec diamond   (slides)

Extreme value statistics: from random matrices to number theory 

On point fields related to Airy processes

Concentration for Coulomb gases and Coulomb transport in- equalities 

The Magnificent Four​

Dynamical universality for random matrices​

  • Yanqi Qiu (Institut de Mathématiques de Toulouse)

Classification of ergodic measures on infinite matrices over non-Archemidean local field

On reproducing kernel Hilbert spaces related to determinantal processes

Conditioned determinantal processes are determinantal 

Determinantal point processes associated with reproducing kernel Hilbert spaces

Summability of 1/N expansions

The Absolute of random walks on the groups 

​Random matrices and canonical systems