Linear response and moderate deviations: hierarchical approach. III

TL;DR

This paper extends the Moderate Deviations Principle to splittable random fields, providing a hierarchical approach that advances understanding for complex dependent structures beyond sums of independent variables.

Contribution

It establishes the MDP for splittable random fields, a significant step forward for dependent random structures, adapting previous frameworks to new versions and terminology.

Findings

MDP now proven for splittable random fields

Hierarchical approach enhances analysis of dependent structures

Updated references and terminology for clarity

Abstract

The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. Here it is established for splittable random fields. Version 2. Adapted to new Version 3 of [2] arXiv:1706.00991. Terminology: "CMS random fields". Numbers of items in [2] updated. References: "response", not "responce". Otherwise unchanged.