Simplification of the majorizing measures method, with development

TL;DR

This paper refines the majorizing measures method for analyzing local structures of random fields, simplifying the approach and improving constant values through generalizations of existing inequalities.

Contribution

It introduces a simplified version of the majorizing measures method with enhanced constants, building on generalized inequalities for better analysis of random fields.

Findings

Simplified the majorizing measures method.

Improved constant values in the analysis.

Extended the method using generalized inequalities.

Abstract

We update, specify, review and develop in this article the classical majorizing measures method for investigation of the local structure of random fields, belonging to X.Fernique and M.Talagrand in order to simplify and improve the constant values. Our considerations based on the generalization of the L.Arnold and P.Imkeller generalization of classical Garsia-Rodemich-Rumsey inequality.