Integrable systems and random matrices

Team members

Tom CLAEYS
Gabriel GLESNER
Olelsandr MINAKOV
Giuilio RUZZA
Pierre VAN MOERBEKE
Meng YANG

Research topics

  • The study of eigenvalues of random matrices.
  • Determinantal point processes, repulsive particle systems, random growth models
  • Asymptotic analysis of orthogonal polynomials and Hankel, Toeplitz and Fredholm determinants.
  • Asymptotic analysis via Riemann-Hilbert problems.
  • Integrable differential equations, such as Painlevé equations and nonlinear wave equations (like the Korteweg-de Vries equation which describes shallow water waves).

Representative publications

  • M. Cafasso and T. Claeys, A Riemann-Hilbert approach to the lower tail of the KPZ equation (arxiv:1910.02493)
  • C. Charlier and T. Claeys, Large gap asymptotics for Airy kernel determinants with discontinuities, Comm. Math. Phys. (2019), https://doi.org/10.1007/s00220-019-03538-w
  • T. Claeys and I. Krasovsky, Toeplitz determinants with merging singularities, Duke Math. Journal 164, no. 15 (2015), 2897-2987
  • M. Adler, Mark, K. Johansson, Kurt, and P. van Moerbeke, Double Aztec diamonds and the tacnode process, Adv. Math. 252 (2014), 518–571
  • T. Claeys, A. Its, and I. Krasovsky, Emergence of a singularity for Toeplitz determinants and Painlevé V, Duke Math. Journal 160, no. 2 (2011), 207-262
  •  P. van Moerbeke, Random and integrable models in mathematics and physics. Random matrices, random processes and integrable systems, 3–130, CRM Ser. Math. Phys., Springer, New York, 2011

Useful links

•    Séminaire GPP, Géométire, Physique, Probabilités.
•    ERC (European Research Council), Projet CRAMIS. •    EOS project PRIMA. •    PAI (Phase VII-18) DYGEST, Pôle d'attraction interuniversitaire, Dynamics, Geometry and Statistical Physics.