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Darboux Transformations and Random Point Processes

Abstract :

In this paper, we describe a general method to derive formulas relating the gap probabilities of some classical determinantal random point processes (Airy, Pearcey, and Hermite) with the gap probability of the same processes with “wanderers”, “inliers”, and “outliers”. In this way, we generalize the Painlevé-like formula found by Baik for the Baik–Ben Arous–Péché distribution to many different cases, both in the one and multi-time setting. The method is not ad hoc and relies upon the notion of Schlesinger transformations for Riemann–Hilbert problems.

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https://hal.archives-ouvertes.fr/hal-01392109
Contributor : Okina Université d'Angers <>
Submitted on : Friday, November 4, 2016 - 10:12:32 AM
Last modification on : Monday, March 9, 2020 - 6:15:54 PM

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Marco Bertola, Mattia Cafasso. Darboux Transformations and Random Point Processes. International Mathematics Research Notices, Oxford University Press (OUP), 2015, 2015 (15), pp.6211-6266. ⟨10.1093/imrn/rnu122⟩. ⟨hal-01392109⟩

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