I will explain the Lyons-Peres conjecture in the theory of determinantal point processes (DPP). This conjecture asks certain completeness of a DPP with orthogonal projection correlation kernel. In a particular case, it asks whether almost surely the random set of zeros of the Gaussian random analytic function is the set of uniqueness for Bergman space.   Recently, in a joint work with Alexander Bufetov and Alexander Shamov, we solve completely the Lyons-Peres conjecture. Our method is based on proving the existence and a new local property of conditional correlation kernels for conditional DPP.

海报