An error bound in the Sudakov-Fernique inequality

Abstract

We obtain an asymptotically sharp error bound in the classical Sudakov-Fernique comparison inequality for finite collections of gaussian random variables. Our proof is short and self-contained, and gives an easy alternative argument for the classical inequality, extended to the case of non-centered processes.

This will appear as a theorem in Robert Adler's new book with Jonathan Taylor on gaussian processes; will not be submitted to any journal in its present form