Dyson's Brownian motions, intertwining and interlacing
Warren, Jon. (2007) Dyson's Brownian motions, intertwining and interlacing. Electronic Journal of Probability, Vol.12 . pp. 573-590. ISSN 1083-6489
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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.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Brownian motion processes|
|Journal or Publication Title:||Electronic Journal of Probability|
|Publisher:||University of Washington. Dept. of Mathematics|
|Number of Pages:||18|
|Page Range:||pp. 573-590|
|Access rights to Published version:||Open Access|
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