Journal Article

Darboux Transformations and Random Point Processes

Marco Bertola and Mattia Cafasso

in International Mathematics Research Notices

Volume 2015, issue 15, pages 6211-6266
Published in print January 2015 | ISSN: 1073-7928
Published online July 2014 | e-ISSN: 1687-0247 | DOI: https://dx.doi.org/10.1093/imrn/rnu122
Darboux Transformations and Random Point Processes

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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.

Journal Article.  18503 words.  Illustrated.

Subjects: Mathematics

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