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. © 2014 The Author(s) 2014. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Darboux Transformations and Random Point Processes / Bertola, M.; Cafasso, M.. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2015:15(2015), pp. rnu122.6211-rnu122.6266. [10.1093/imrn/rnu122]

Darboux Transformations and Random Point Processes

Bertola, M.;
2015-01-01

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. © 2014 The Author(s) 2014. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
2015
2015
15
6211
6266
10.1093/imrn/rnu122
https://arxiv.org/abs/1401.4752
https://academic.oup.com/imrn/article/2015/15/6211/692703
Bertola, M.; Cafasso, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11934
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