Determinantal point processes: quasi-symmetries, minimality, and interpolation

Alexander Bufetov (CNRS & Institut Institut de Mathématiques de Marseille & Steklov, IITP RAS)

16-Jun-2021, 15:15-16:15 (3 years ago)

Abstract: What is the relation between a determinantal point process and the Hilbert space that governs it? For the sine-process of Dyson, almost every realization with one particle removed is a complete and minimal set for the Paley-Wiener space, while if two particles are removed, then one obtains azero set for the Paley-Wiener space. Quasi-invariance of the sine-process under compactly supported diffeomorphisms plays a key role. In joint work with Qiu, the Patterson-Sullivan construction is used to interpolate Bergman functions from the zero set of a random series with independent complex Gaussian entries. The determinantal property, due to Peres and Virg, and the invariance of the zero set under the isometries of the Lobachevsky plane play a key role.

Mathematics

Audience: researchers in the discipline


Azat Miftakhov Day

Series comments: The conference begins with an opening speech by Cédric Villani 15 minutes before Viazovska's lecture. The webinar will be broadcast live on the website (https://caseazatmiftakhov.org/) and on the youtube channel DayAzatMiftakhov (https://www.youtube.com/channel/UCyPwe0Fv3BcCz7V0MPeDN6Q/live).

Organizer: Ahmed Abbes*
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