## The Annals of Probability

### Dynamics of the McKean-Vlasov Equation

Terence Chan

#### Abstract

This note studies the deterministic flow of measures which is the limiting case as $n \rightarrow \infty$ of Dyson's model of the motion of the eigenvalues of random symmetric $n \times n$ matrices. Though this flow is nonlinear, highly singular and apparently of Wiener-Hopf type, it may be solved explicitly without recourse to Wiener-Hopf theory. The solution greatly clarifies the role of the famous Wigner semicircle law.

#### Article information

Source
Ann. Probab., Volume 22, Number 1 (1994), 431-441.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988866

Digital Object Identifier
doi:10.1214/aop/1176988866

Mathematical Reviews number (MathSciNet)
MR1258884

Zentralblatt MATH identifier
0798.60029

JSTOR