Sudakov minoration for products of radial-type log concave measures

TL;DR

This paper establishes Sudakov minoration for canonical processes derived from radial-type log-concave measures, advancing the understanding of lower bounds for stochastic process suprema.

Contribution

It proves Sudakov minoration for processes based on radial-type log-concave measures, a novel extension in the study of stochastic process bounds.

Findings

Proves Sudakov minoration for radial-type log-concave measures

Provides a foundation for characterizing process supremum expectations

Enhances tools for analyzing stochastic processes with specific measure types

Abstract

The first step to study lower bounds for a stochastic process is to prove a special property - Sudakov minoration. The property means that if a certain number of points from the index set are well separated then we can provide an optimal type lower bound for the mean value of the supremum of the process. Together with the generic chaining argument the property can be used to fully characterize the mean value of the supremum of the stochastic process. In this article we prove the property for canonical processes based on radial-type log concave measures.