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May 30, 2018, Professor Sasamoto's Seminar, Tokyo Institute of Technology  


Determinantal point processes and extrapolation

A. I. Bufetov
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Abstract: In joint work with Yanqi Qiu and Alexander Shamov we prove that the zero set of a Gaussian Analytic Function is almost surely a uniqueness set in the Bergman space on the unit disc — equivalently, that any square-integrable holomorphic function is uniquely determined by its restriction to our set. By the Peres-Virag theorem, our random set is a determinantal point process governed by the Bergman kernel. The key lemma is that conditioning preserves the determinantal property. In subsequent joint work with Yanqi Qiu, we show that the Patterson-Sullivan construction recovers the value of any Hardy function at any point of the disc from its restriction to a random configuration of the determinant point process with the Bergman kernel.

Language: English

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