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Mathematical Sciences Research Institute

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Program

Universality and Integrability in Random Matrix Theory and Interacting Particle Systems August 16, 2021 to December 17, 2021
Organizers LEAD Ivan Corwin (Columbia University), Percy Deift (New York University, Courant Institute), Ioana Dumitriu (University of Washington), Alice Guionnet (École Normale Supérieure de Lyon), Alexander Its (Indiana University-Purdue University Indianapolis), Herbert Spohn (Technische Universität München), Horng-Tzer Yau (Harvard University)
Description
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The past decade has seen tremendous progress in understanding the behavior of large random matrices and interacting particle systems. Complementary methods have emerged to prove universality of these behaviors, as well as to probe their precise nature using integrable, or exactly solvable models. This program seeks to reinforce and expand the fruitful interaction at the interface of these areas, as well as to showcase some of the important developments and applications of the past decade.
Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • Random matrix theory

  • Numerical linear algebra

  • condition number

  • Anderson localization

  • spectral graph theory

  • Beta ensembles

  • log-gases

  • spin glasses

  • Neural networks

  • Principal component analysis

  • Sample covariance matrix

  • free probability

  • Dyson Brownian motion

  • Non-normal matrices

  • Orthogonal polynomials

  • Hankel determinants

  • Toepliz determinants

  • L-functions

  • Airy process

  • Sine process

  • Determinantal point processes

  • Kardar-Parisi-Zhang universality

  • Asymmetric simple exclusion process

  • Random growth model

  • Interacting particle system

  • random tilings

  • Gaussian free field

  • Directed polymer

  • Last passage percolation

  • Bethe ansatz

  • Six vertex model

  • Yang-Baxter equation

  • Arctic circle theorem

  • Tracy-Widom distribution

  • Stochastic partial differential equation

  • Stochastic heat equation

  • Stochastic Burgers equation

  • Integrable probability

  • Symmetric polynomials

  • Painleve transcendents

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Programmatic Workshops
October 18, 2021 - October 22, 2021 Integrable structures in random matrix theory and beyond