Title :

On some random thin sets of integers

Author(s) :

Li, Daniel [Auteur]
Laboratoire de Mathématiques de Lens [LML]
Queffélec, Hervé [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rodriguez-Piazza, Luis [Auteur]

Journal title :

Proceedings of the American Mathematical Society

Pages :

141 - 150

Publisher :

American Mathematical Society

Publication date :

2008

ISSN :

0002-9939

English keyword(s) :

Boucheron-Lugosi-Massart's deviation inequality
$\Lambda (q)$-sets
$p$-Rider sets
Rosenthal sets
selectors
sets of uniform convergence

HAL domain(s) :

Mathématiques [math]/Analyse fonctionnelle [math.FA]

English abstract : [en]

We show how different random thin sets of integers may have different behaviour. First, using a recent deviation inequality of Boucheron, Lugosi and Massart, we give a simpler proof of one of our results in {\sl Some new ...
Show more >We show how different random thin sets of integers may have different behaviour. First, using a recent deviation inequality of Boucheron, Lugosi and Massart, we give a simpler proof of one of our results in {\sl Some new thin sets of integers in Harmonic Analysis, Journal d'Analyse Mathématique 86 (2002), 105--138}, namely that there exist $\frac{4}{3}$-Rider sets which are sets of uniform convergence and $\Lambda (q)$-sets for all $q < \infty $, but which are not Rosenthal sets. In a second part, we show, using an older result of Kashin and Tzafriri that, for $p > \frac{4}{3}$, the $p$-Rider sets which we had constructed in that paper are almost surely ot of uniform convergence.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL