Some remarks on the Sudakov minoration

TL;DR

This paper extends the Sudakov minoration, originally for Gaussian processes, to dependent settings involving log-concave random variables, discussing methods to establish lower bounds on supremum expectations.

Contribution

It generalizes Sudakov minoration to dependent log-concave variables and explores proof techniques for this broader context.

Findings

Sudakov minoration can be extended to dependent log-concave variables.

Methods for proving the generalized property are discussed.

The paper provides insights into lower bounds for dependent processes.

Abstract

In this paper we discuss Sudakov type minoration for the dependent setting. Sudakov minoration is a well known property first proved for centered Gaussian processes which states that for well separated points there is a natural lower bound on the expectation of the supremum of such a process. We generalize this concept for the dependent setting where we consider log concave random variables and then discuss methods of proving the property.