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Determinantal point processes conditioned on randomly incomplete configurations

Gabriel Glesner
Monday, January 31, 2022 - 17:00 to 18:00

We consider a marked point process with independent binomial marks 0 and 1. In our context of randomly incomplete configuration, we interpret the mark 1 points as detected while the mark 0 ones are unobserved. We then define the point process consisting of the undetected particles conditioned on a finite observation, i.e a finite configuration of mark 1 points. When the ground process is determinantal, so is every one of the aforementioned point processes. Furthermore, important subclasses of determinantal point processes, namely the ones induced by projections and k-integrable kernels, are also preserved under this conditioning. In the latter case, the transformation can be characterised using a Riemann-Hilbert problem which can be seen as a combination of the celebrated method of Its, Izergin Korepin and Slavnov, with a discrete version of this method. This is based on joint work with Tom Claeys (UCLouvain) []

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