【学术报告】Point Processes and Interpolation

• 主讲人：Alexander BUFETOV (CNRS Steklov IITP RAS)
• 时间：周四15:00-16:00，2021-04-22
• 地点：online

Beijing-Saint Petersburg Mathematics Colloquium (online)

摘要（Abstract） 

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? In the case of the zero set of the Gaussian analytic function, or, in other words, the determinantal point process governed by the Bergman kernel, in joint work with Qiu, the Patterson-Sullivan construction is used for uniform interpolation in dense subspaces of the Bergman space. The invariance of our point process under Lobachevskian isometries plays a key rôle.
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.

主讲人简介（Bio）

Alexander Bufetov is an expert in Ergodic Theory, Probability, Dynamical Systems and Statistics.
He graduated from Moscow State University being student of Acad. Ya. Sinai, one of the worldwide greatest experts in Ergodic Theory. Later on, he has got his PhD from Princeton University. In 2011 he became Doctor of Sciences. In 2015 he won the prestigious Sofia Kovalevskaya price and, thereafter, has got a honorary degree of ‘Professor of Russian Academy of Science’. He is an author of an impressive number of outstanding results https://scholar.google.com/citations?user=nAkXSowAAAAJ&hl=ru.
Prof. Bufetov had a wide range of prestigious positions: at Mathematical Institute of Russian Academy of Sciences, Higher School of Economics, Rice Univeristy, Chebyshev Laboratory at Saint Petersburg State University etc.  Now he is working at University Aix-Marseille at CNRS Director position.