Conference: ProbabLY ON Random Matrices (ENS Lyon)

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Date(s) - 02/04/2017 - 06/04/2017
0 h 00 min

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The conference will focus on active areas of Random Matrix Theory :

Alexander’s talk on Tuesday (april 4th at 14:00-14:45) : «Conditional measures of determinental point processes: the Gibbs property and the Lyons-Peres Conjecture»

How do determinantal point processes behave under conditioning with respect to fixing the configuration in a subset of the phase space? The talk will first address this question for specific examples such as the sine-process or the process with the Bessel kernel, where one can explicitl y write the analogue of the Gibbs property in our situation. We will then consider processes induced by general self-adjoint kernels, for which, in joint work with Yanqi Qiu and Alexander Shamov, it is shown that conditional measures of such processes are themselves determinantal and gove rned by self-adjoint kernels, that thethe tail sigma-algebra for such proces ses is trivial (a result independently and by a completely different method obtained by Osada–Osada) and proof is given of the Lyons-Peres conjecture o n completeness of the system of kernels sampled at the particles of a random configuration. The talk is based on the preprint arXiv:1605.01400 as well as on the preprint arXiv:1612.06751 joint with Yanqi Qiu and Alexan der Shamov.

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