Some deviation inequalities

Abstract

We introduce a concentration property for probability measures on $R^n$, which we call Property~($\tau$); we show that this property has an interesting stability under products and contractions (Lemmas 1,~2,~3). Using property~($\tau$), we give a short proof for a recent deviation inequality due to Talagrand. In a third section, we also recover known concentration results for Gaussian measures using our approach.}