A note on talagrand’s concentration inequality

Abstract

In this paper we revisit Talagrand’s proof of concentration inequality for empirical processes. We give a different proof of the main technical lemma that garantees the existence of a certain kernel. Moreover, we generalize the result of Talagrand to a family of kernels which in one particular case allows us to produce the Poissonian bound without using the truncation argument. In section 2 we give some examples of application of the abstract concentration inequality to empirical processes that demonstrate some interesting properties of Talagrand’s kernel method. © 2001 Rocky Mountain Mathematics Consortium.