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From the Pearcey to the Airy process. (English) Zbl 1231.60107

Summary: Putting dynamics into random matrix models leads to finitely many nonintersecting Brownian motions on the real line for the eigenvalues, as was discovered by F. J. Dyson [J. Math. Phys. 3, 1191–1198 (1962; Zbl 0111.32703)]. 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.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60B20 Random matrices (probabilistic aspects)

Citations:

Zbl 0111.32703
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