×

On concentration of self-bounding functions. (English) Zbl 1189.60040

Summary: We prove some new concentration inequalities for self-bounding functions using the entropy method. As an application, we recover Talagrand’s convex distance inequality. The new Bernstein-like inequalities for self-bounding functions are derived thanks to a careful analysis of the so-called Herbst argument. The latter involves comparison results between solutions of differential inequalities that may be interesting in their own right.

MSC:

60E15 Inequalities; stochastic orderings
60C05 Combinatorial probability
28A35 Measures and integrals in product spaces
05C80 Random graphs (graph-theoretic aspects)
PDF BibTeX XML Cite
Full Text: DOI EuDML EMIS