Concentration via chaining method and its applications

Abstract

In this paper we study the regularity of paths in terms of properties of admissible nets. We show the right concentration inequality above the modulus of continuity. Using the approach we prove the Bernstein type inequality for the empirical processes. Therefore we obtain the best form of concentration for processes studied recently by Mendelson and Paouris. Results of this type are of importance in the compressed sensing theory.