Multi angle A functional limit theorem for the sine-process
Auteurs : Dymov, Andrey (Auteur de la Conférence)
CIRM (Editeur )
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Résumé : It is well-known that a large class of determinantal processes including the sine-process satisfies the Central Limit Theorem. For many dynamical systems satisfying the CLT the Donsker Invariance Principle also takes place. The latter states that, in some appropriate sense, trajectories of the system can be approximated by trajectories of the Brownian motion. I will present results of my joint work with A. Bufetov, where we prove a functional limit theorem for the sine-process, which turns out to be very different from the Donsker Invariance Principle. We show that the anti-derivative of our process can be approximated by the sum of a linear Gaussian process and small independent Gaussian fluctuations whose covariance matrix we compute explicitly.Codes MSC :
60F05 - Central limit and other weak theorems
60G55 - Point processes
60G60 - Random fields