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Riemann-Hilbert approach to gap probabilities of determinantal point processes. The Generalized Bessel case.

Le : 20/05/2015 14h30
Par : Manuela Girotti (Université Catholique de Louvain)
Lieu : I 001
Lien web :
Résumé : We will consider a model of self-avoiding random paths. This is an example of a determinantal point process and it is known that the expectations of occupation numbers of subsets of the configuration space are expressible in terms of Fredholm determinants. For particular cases, the evaluation of such Fredholm determinants is strictly related to the study of suitable Riemann-Hilbert problems which allow to connect these probabilities with the theory of isomonodromic deformations and tau-function. As an example, we will focus on the case of the Generalized Bessel process.