English
Classification and statistics of cut-and-project sets
Virtualconference
Auteurs : Weiss, Barak (Auteur de la Conférence)
CIRM (Editeur )
CIRM (Editeur )
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Résumé :
We introduce a class of so-called "Ratner-Marklof-Strombergsson measures". These are probability measures supported on cut-and-project sets in Euclidean space of dimension d>1 which are invariant and ergodic for the action of the groups ASL_d(R) or SL_d(R) (affine or linear maps preserving orientation and volume). We classify the measures that can arise in terms of algebraic groups and homogeneous dynamics. Using the classification, we prove analogues of results of Siegel, Weil and Rogers about a Siegel summation formula and identities and bounds involving higher moments. We deduce results about asymptotics, with error estimates, of point-counting and patchcounting for typical cut-and-project sets. Joint work with Rene Ruehr and Yotam Smilansky.
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 01/12/2020 Date de captation : 23/11/2020 Sous collection : Research talks arXiv category : Dynamical Systems Domaine : Number Theory ; Mathematical Physics ; Probability & Statistics ; Dynamical Systems & ODE Format : MP4 (.mp4) - HD Durée : 00:49:22 Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-23_Barak Weiss.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireOrganisateurs de la rencontre : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Année de la rencontre : 2020 URL Congrès : https://www.chairejeanmorlet.com/2256.html
Données de citation
DOI : 10.24350/CIRM.V.19690003Citer cette vidéo: Weiss, Barak (2020). Classification and statistics of cut-and-project sets. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19690003 URI : http://dx.doi.org/10.24350/CIRM.V.19690003 |
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Bibliographie
