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SEMINARS |
Steklov Mathematical Institute Seminar
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Chaos and order for determinantal point processes A. I. Bufetov |
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Abstract: Determinantal point processes arise in combinatorics, representation theory and mathematical physics, specifically random matrix theory. Our processes are chaotic: the Central Limit Theorem holds (Costin-Lebowitz, Soshnikov), and so does its functional analogue (Dymov and the speaker), the Kolmogorov 0-1 law also holds (Lyons, Osada-Osada, Qiu, Shamov and the speaker). At the same time, particles of our random configurations interact at infinite distance, as is shown by the Ghosh-Peres rigidity property or the explicit form of conditional measures for our processes found by the speaker. As shown by Qiu, Shamov and the speaker, almost every realization of a determinantal point process is a uniqueness set for the governing reproducing kernel Hilbert space, for instance, the Bergman space. While partial results are given by the Patterson-Sullivan construction, the general question of simultaneous extrapolation of Bergman functions from their restrictions to our random configuration remains largely open. |