Point processes and interpolation

Alexander Bufetov
I2M, Aix-Marseille Université

Date(s) : 12/04/2021   iCal
14 h 00 min - 15 h 00 min

The Kotelnikov theorem recovers  a Paley-Wiener function from its restriction onto an arithmetic progression. A Paley-Wiener function can also be recovered from its restriction onto a realization of the sine-process with one particle removed. If no particles are removed, then the possibility of such interpolation for the sine-process is due to Ghosh, for general determinantal point processes governed by orthogonal projections, to Qiu, Shamov and the speaker. If two particles are removed, then there exists a nonzero Paley-Wiener function vanishing at all the remaining particles.

How explicitly to interpolate a function  belonging to Hilbert space that admits a reproducing kernel, given the restriction of our function onto  a realization of the determinantal pont process governed by the kernel? For the sine-process, the Ginibre process, the determinantal point process  with the Bessel kernel and  the determinantal point process  with the Airy kernel, A.A. Borichev, A.V. Klimenko and the speaker proved that if the function decays as a sufficiently high negative power of the distance to the origin, then the answer is given by the Lagrange interpolation formula.

Schedule, direct link to the virtual room and all relevant information:

Lecture room link: https://bbb1.cirm-math.fr/b/org-n9z-3je

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