Determinantal point processes and spaces of analytic functions (Lecture 1)

The mini-course is devoted to recently found links between the theory of determinantal point processes and reproducing kernel Hilbert spaces of analytic functions like de Branges or Fock spaces. We concentrate on processes possessing the quasi-invariance property which is shared by many important processes (Sine process, Airy and Bessel processes, the Gamma kernel process etc). This property turns out to be related to division properties for the corresponding spaces of analytic functions.