From the Pearcey to the Airy process

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.

21 pages, 2 figures

References in corpus (3)

• The Pearcey Process
• Differential Equations for Dyson Processes
• PDEs for the joint distributions of the Dyson, Airy and Sine processes

Cited by in corpus (8)

• Nonintersecting random walks in the neighborhood of a symmetric tacnode
• Spectrum of deformed random matrices and free probability
• Asymptotics of Fredholm determinant associated with the Pearcey kernel
• Nonlinear PDEs for gap probabilities in random matrices and KP theory
• The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation
• Pearcey universality at cusps of polygonal lozenge tiling
• Fluctuations at the edges of the spectrum of the full rank deformed GUE
• Double Interlacing in Random Tiling Models