Skip to Main content Skip to Navigation
New interface
Preprints, Working Papers, ...

Random matrices

Abstract : We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of algebraic geometry, loop equations and their solution using topological recursion, orthogonal polynomials and their relation with integrable systems. Each approach provides its own definition of the spectral curve, a geometric object which encodes all the properties of a model. We also introduce the two peripheral subjects of counting polygonal surfaces, and computing angular integrals.
Complete list of metadata

Cited literature [62 references]  Display  Hide  Download
Contributor : Emmanuelle De Laborderie Connect in order to contact the contributor
Submitted on : Thursday, January 7, 2016 - 10:29:13 AM
Last modification on : Monday, December 13, 2021 - 9:16:04 AM
Long-term archiving on: : Friday, April 8, 2016 - 1:14:10 PM


Files produced by the author(s)


  • HAL Id : cea-01252029, version 1
  • ARXIV : 1510.04430


Bertrand Eynard, Taro Kimura, Sylvain Ribault. Random matrices. {date}. ⟨cea-01252029⟩



Record views


Files downloads