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Article Dans Une Revue Electronic Journal of Probability Année : 2011

From the Pearcey to the Airy process

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Mark Adler
  • Fonction : Auteur
Pierre van Moerbeke
  • Fonction : Auteur


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 toapproximate 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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hal-03031616 , version 1 (30-11-2020)



Mark Adler, Mattia Cafasso, Pierre van Moerbeke. From the Pearcey to the Airy process. Electronic Journal of Probability, 2011, 16, pp.1048 - 1064. ⟨10.1214/EJP.v16-898⟩. ⟨hal-03031616⟩
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