This is an announcement for the paper "Combinatorics of random processes and sections of convex bodies" by Mark Rudelson and Roman Vershynin. Abstract: We find a sharp combinatorial bound for the metric entropy of sets in R^n and general classes of functions. This solves two basic combinatorial conjectures on the empirical processes. 1. A class of functions satisfies the uniform Central Limit Theorem if the square root of its combinatorial dimension is integrable. 2. The uniform entropy is equivalent to the combinatorial dimension under minimal regularity. Our method also constructs a nicely bounded coordinate section of a symmetric convex body in R^n. In the operator theory, this essentially proves for all normed spaces the restricted invertibility principle of Bourgain and Tzafriri. Archive classification: Functional Analysis; Probability Theory Mathematics Subject Classification: 46B09, 60G15, 68Q15 Remarks: 49 pages The source file(s), rv-processes.tex: 122610 bytes, is(are) stored in gzipped form as 0404192.gz with size 38kb. The corresponding postcript file has gzipped size 150kb. Submitted from: vershynin@math.ucdavis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0404192 or http://arXiv.org/abs/math.FA/0404192 or by email in unzipped form by transmitting an empty message with subject line uget 0404192 or in gzipped form by using subject line get 0404192 to: math@arXiv.org.