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2011 From the Pearcey to the Airy Process.
Mark Adler, Mattia Cafasso, Pierre van Moerbeke
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Electron. J. Probab. 16: 1048-1064 (2011). DOI: 10.1214/EJP.v16-898

Abstract

Putting dynamics into random matrix models leads to finitely many nonintersecting Brownian motions on the real line for the eigenvalues, as was discovered by Dyson. Applying scaling limits to the random matrix models, combined with Dyson's dynamics, then leads to interesting, infinite-dimensional diffusions for the eigenvalues. This paper studies the relationship between two of the models, namely the Airy and Pearcey processes and more precisely shows how to approximate the multi-time statistics for the Pearcey process by the one of the Airy process with the help of a PDE governing the gap probabilities for the Pearcey process.

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Mark Adler. Mattia Cafasso. Pierre van Moerbeke. "From the Pearcey to the Airy Process.." Electron. J. Probab. 16 1048 - 1064, 2011. https://doi.org/10.1214/EJP.v16-898

Information

Accepted: 1 June 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1231.60107
MathSciNet: MR2820069
Digital Object Identifier: 10.1214/EJP.v16-898

Subjects:
Primary: 60K35
Secondary: 60B20

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Vol.16 • 2011
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