Free analysis and random matrices - Archive ouverte HAL Access content directly
Journal Articles Japanese Journal of Mathematics Year : 2016

Free analysis and random matrices

(1)
1

Abstract

We describe the Schwinger-Dyson equation related with the free difference quotient. Such an equation appears in different fields such as combinatorics (via the problem of the enumeration of planar maps), operator algebra (via the definition of a natural integration by parts in free probability), in classical probability (via random matrices or particles in repulsive interaction). In these lecture notes, we shall discuss when this equation uniquely defines the system and in such a case how it leads to deep properties of the solution. This analysis can be extended to systems which approximately satisfy these equations, such as random matrices or Coulomb gas interacting particle systems.
Fichier principal
Vignette du fichier
Takagi4.pdf (277.26 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

ensl-01400950 , version 1 (22-11-2016)

Identifiers

Cite

Alice Guionnet. Free analysis and random matrices. Japanese Journal of Mathematics, 2016, 11 (1), pp.33-68. ⟨10.1007/s11537-016-1489-1⟩. ⟨ensl-01400950⟩
174 View
159 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More