This is an announcement for the paper "On some random thin sets of integers" by Daniel Li, Herve Queffelec, Luis Rodriguez-Piazza.

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 {\sl Some new thin sets of integers in Harmonic Analysis, Journal d'Analyse Math'ematique 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.

Archive classification: math.FA

Mathematics Subject Classification: 43 A 46 ; 42 A 55 ; 42 A 61

Citation: Proceedings of the American Mathematical Society 136, 1 (2008) 141

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