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The determinantal point processes arise from many branches of areas such as random matrices, representation theory, random graphs and zeros of holomorphic functions etc.
In this talk, I will briefly recall the basic materials in the theory of determinantal point processes and then will discuss some results concerning the conditional measures, rigidity property and the Olshanski’s problem on this area.
The talk will be based on several works joint with Alexander Bufetov, Alexander Shamov and Shilei Fan.