Title: Marking and conditioning of determinantal point processes
Speaker: Tom Claeys (Université catholique de Louvain, Belgium)
Speaker's URL: https://perso.uclouvain.be/tom.claeys/
Abstract: Determinantal point processes are a class of point processes for which statistics are encoded in the kernel of a locally trace class operator. Of particular interest are determinantal point processes induced by orthogonal projections, like orthogonal polynomial ensembles and their scaling limits like the sine, Airy, and Bessel determinantal point processes. We will describe a transformation of determinantal point processes involving marking and conditioning, and we will explain how the associated operators and kernels behave under this transformation. I will show that this transformation is closely connected with a remarkable rigidity result, with tail distributions of the KPZ equation, and with integrable PDEs. The talk will be based on joint work with Gabriel Glesner.