Open Access
2007 Dyson's Brownian motions, intertwining and interlacing
Jon Warren
Author Affiliations +
Electron. J. Probab. 12: 573-590 (2007). DOI: 10.1214/EJP.v12-406


A reflected Brownian motion in the Gelfand-Tsetlin cone is used to construct Dyson's process of non-colliding Brownian motions. The key step of the construction is to consider two interlaced families of Brownian paths with paths belonging to the second family reflected off paths belonging to the first. Such families of paths are known to arise in the Arratia flow of coalescing Brownian motions. A determinantal formula for the distribution of coalescing Brownian motions is presented.


Download Citation

Jon Warren. "Dyson's Brownian motions, intertwining and interlacing." Electron. J. Probab. 12 573 - 590, 2007.


Accepted: 1 May 2007; Published: 2007
First available in Project Euclid: 1 June 2016

zbMATH: 1127.60078
MathSciNet: MR2299928
Digital Object Identifier: 10.1214/EJP.v12-406

Primary: 60J65
Secondary: 60J35 , 60J60

Keywords: Coalescing Brownian motions , Gelfand-Tsetlin cone , intertwining , non-colliding Brownian motions

Vol.12 • 2007
Back to Top