A sharp concentration inequality with applications

We derive a new general concentration‐of‐measure inequality. The concentration inequality applies, among others, to configuration functions as defined by Talagrand and also to combinatorial entropies such as the logarithm of the number of increasing subsequences in a random permutation and to Vapnik‐Chervonenkis (VC) entropies. The results find direct applications in statistical learning theory, substantiating the possibility to use the empirical VC entropy in penalization techniques. © 2000 John Wiley & Sons, Inc. Random Struct. Alg., 16: 277–292, 2000