Random matrices and determinantal process / Matrices aléatoires. Processus déterminantaux

Collection Random matrices and determinantal process / Matrices aléatoires. Processus déterminantaux

Organisateur(s) Bufetov, Alexander ; Chhaibi, Reda ; Grava, Tamara ; Kuijlaars, Arno ; Krasovsky, Igor ; Nikitin, Pavel ; Savin, Dmitry

Date(s) 27/02/2017 - 03/03/2017

URL associée http://conferences.cirm-math.fr/1715.html

00:00:00 / 00:00:00

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A functional limit theorem for the sine-process

De Andrey Dymov

Apparaît également dans la collection : Exposés de recherche

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.

Informations sur la vidéo

Date de captation 28/02/2017
Date de publication 08/03/2017
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19134403
Citer cette vidéo Dymov, Andrey (28/02/2017). A functional limit theorem for the sine-process . CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19134403
URL https://dx.doi.org/10.24350/CIRM.V.19134403

Domaine(s)

Bibliographie

Bufetov, A.I., & Dymov, A.V. (2016). A functional limit theorem for the sine-process. <arXiv:1701.00111> - https://arxiv.org/abs/1701.00111

Codes MSC

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