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The Airy point process and a system of coupled Painlevé II equations

Speaker: 
Antoine Doeraene
Institution: 
Université Catholique de Louvain
Schedule: 
Monday, May 28, 2018 - 16:00
Location: 
A-134
Abstract: 

The Airy point process describes the behaviour of the few largest eigenvalues in the Gaussian Unitary Ensemble. In 1992, Tracy and Widom established the celebrated connection between the probability distribution of the largest particle of the Airy point process, and the Painlevé II equation. This distribution can be generalized in a rather simple way, and allows to actually describes the joint probability distribution of any choice of k ordered particles. This generalization involves a system of differential equations that exhibits Painlevé II-like features. We will also see how this generalization applies to another point process, the Bessel point process.

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