Concentration for independent random variables with heavy tails

Franck Barthe (1) , Patrick Cattiaux (2, 3) , Cyril Roberto (4)

1 LSP - Laboratoire de Statistique et Probabilités
2 MODAL'X - Modélisation aléatoire de Paris X
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
4 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish concentration inequalities for finite sequences of $n$ independent copies, with good dependence in $n$.

Mots clés: concentration; weak Poincaré inequality; Hardy inequality

Domaines: Probabilités [math.PR]

Franck Barthe, Patrick Cattiaux, Cyril Roberto. Concentration for independent random variables with heavy tails. 2005. ⟨hal-00004959⟩