The Annals of Probability

Dynamics of the McKean-Vlasov Equation

Terence Chan

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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
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G57: Random measures 45E10: Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35] 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]

Keywords
Eigenvalues of random matrices Wigner semicircle law measure-valued diffusion McKean-Vlasov equation

Citation

Chan, Terence. Dynamics of the McKean-Vlasov Equation. Ann. Probab. 22 (1994), no. 1, 431--441. doi:10.1214/aop/1176988866. https://projecteuclid.org/euclid.aop/1176988866


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