多复变与复几何研讨班：General theory on determinantal point processes

摘  要：We shall give a brief introduction to the basic materials in the theory of determinantal point processes.

摘  要：We are going to talk about the Olshanski open problem on determing whether two determinantal point processes are absolutely continuous or mutually singular.

摘  要：We are going to talk about some classical limit theorems for determinantal point processes including law of large numbers and central limit theorems.

摘  要：We outline some important connections between determinantal point processes and the Bergman spaces of holomorphic functions in domains of one dimensional complex plane as well as of  higher dimensional complex Euclidean spaces.

摘  要：We are going to talk about the Lyons-Peres completeness conjecture on determinantal point processes generated by reproducing kernel Hilbert spaces, in particular, we mainly focus on weighted Bergman spaces of holomorphic functions.

摘  要：We are going to talk about our result on the random Patterson-Sullivan reconstruction of Bergman holomorphic functions in complex unit balls in the setting of determinantal point processes induced by the standard Bergman kernels.