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St. Petersburg Seminar on Representation Theory and Dynamical Systems
October 19, 2022 16:00, St. Petersburg, PDMI, room 311 (nab. r. Fontanki, 27)
 


The Gaussian multiplicative chaos for the sine-process

A. I. Bufetov

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Abstract: To almost every realization of the sine-process one naturally assigns a random entire function, the analogue of the Euler product for the sine, the scaling limit of ratios of characteristic polynomials of a random matrix. The main result of the talk is that the square of the absolute value of our random entire function converges to the Gaussian multiplicative chaos. As a corollary, one obtains that almost every realization with one particle removed is a complete and minimal set for the Paley-Wiener space, whereas if two particles are removed, then the resulting set is a zero set for the Paley-Wiener space. Quasi-invariance of the sine-process under compactly supported diffeomorphisms of the line plays a key role.
 
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