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Abstract:
We obtain exponential concentration inequalities for sub-additive
functions of independent random variables under weak conditions on the
increments of those functions, like
the existence of exponential moments for these increments.
As a consequence of these general inequalities, we obtain refinements
of Talagrand's inequality for empirical processes and new
bounds for randomized empirical processes.
These results are obtained by further developing the entropy method
introduced by Ledoux.
