The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation

Abstract : We express the gap probabilities of the tacnode process as the ratio of two Fredholm determinants; the denominator is the standard Tracy-Widom distribution, while the numerator is the Fredholm determinant of a very explicit kernel constructed with Airy functions and exponentials. The formula allows us to apply the theory of numerical evaluation of Fredholm determinants and thus produce numerical results for the gap probabilities. In particular we investigate numerically how, in different regimes, the Pearcey process degenerates to the Airy one, and the tacnode degenerates to the Pearcey and Airy ones.
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Article dans une revue
Random Matrices, Theory and Applications (RMTA), 2013
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https://hal.archives-ouvertes.fr/hal-00802309
Contributeur : Mattia Cafasso <>
Soumis le : mardi 19 mars 2013 - 15:22:28
Dernière modification le : lundi 5 février 2018 - 15:00:03

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  • HAL Id : hal-00802309, version 1
  • ARXIV : 1303.2894

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M. Bertola, M. Cafasso. The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation. Random Matrices, Theory and Applications (RMTA), 2013. 〈hal-00802309〉

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