Linear response and moderate deviations: hierarchical approach. I

TL;DR

This paper develops a hierarchical approach to establish the Moderate Deviations Principle (MDP) for a new class of random processes, extending understanding from sums of independent variables to more complex stationary sequences and potentially random fields.

Contribution

It introduces a novel hierarchical method to prove the MDP for a broader class of random processes, advancing the theoretical framework.

Findings

MDP established for new class of random processes

Approach shows promise for application to random fields

Extends understanding of moderate deviations beyond independent variables

Abstract

This is basically a polished presentation for Sections 1,2 of arXiv:0801.1050. 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 a new class of random processes. The approach is promising also for random fields.