Darboux transformations and random point processes.

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–Péche ́ distribution to many different cases, both in the one and multi–time case. The method is not ad-hoc and relies upon the notion of Schlesinger transformations for Riemann–Hilbert problems