On some random thin sets of integers |
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| Authors: | Daniel Li Hervé Queffé lec Luis Rodrí guez-Piazza |
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| Institution: | Université d'Artois, Laboratoire de Mathématiques de Lens EA 2462--FR 2956, Faculté des Sciences Jean Perrin, 23, rue J. Souvraz SP 18, F-62307 Lens Cedex, France ; Laboratoire Paul Painlevé UMR CNRS 8524, U.F.R. de Mathématiques Pures et Appliquées, Bât. M2, Université des Sciences et Technologies de Lille 1, F-59665 Villeneuve d'Ascq Cedex, France ; Universidad de Sevilla, Facultad de Matemáticas, Departamento de Análisis Matemático, Apartado de Correos 1160, 41080 Sevilla, Spain |
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| Abstract: | 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 Some new thin sets of integers in harmonic analysis, Journal d'Analyse Mathématique 86 (2002), 105-138, namely that there exist  -Rider sets which are sets of uniform convergence and  -sets for all  but which are not Rosenthal sets. In a second part, we show, using an older result of Kashin and Tzafriri, that, for  , the  -Rider sets which we had constructed in that paper are almost surely not of uniform convergence. |
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| Keywords: | Boucheron-Lugosi-Massart deviation inequality $\Lambda (q)$-sets $p$-Rider sets Rosenthal sets selectors sets of uniform convergence |
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