An error bound in the Sudakov-Fernique inequality

TL;DR

This paper provides a precise error bound for the Sudakov-Fernique inequality in Gaussian processes, extending the classical result to non-centered cases with a concise proof.

Contribution

It introduces an asymptotically sharp error bound for the Sudakov-Fernique inequality, including a simplified proof and extension to non-centered Gaussian processes.

Findings

Established a sharp error bound for Gaussian process comparisons.

Extended the inequality to non-centered processes.

Provided a concise, self-contained proof.

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.