Linear response and moderate deviations: hierarchical approach. V

TL;DR

This paper establishes the Moderate Deviations Principle for certain planar random fields derived from Gaussian fields, advancing understanding of deviations in complex stochastic systems and their zeros.

Contribution

It extends the Moderate Deviations Principle to planar random fields formed from Gaussian fields, including applications to zeros of Gaussian Entire Functions.

Findings

MDP established for specific planar random fields

Application to zeros of Gaussian Entire Functions

Enhanced understanding of deviations in random fields

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 some planary random fields of the form $ X_t = \psi(G_t) $ obtained from a Gaussian random field $ G_t $ via a function $ \psi $, and consequently, for zeroes of the Gaussian Entire Function. Version 2: Appendix "Reader's guide to parts I-V" added. Minor changes, as follows. Formulations corrected: (2.1), 3.12(b), 4.5. Proofs corrected: 2.5, 2.6, 3.12, 3.16, 3.19, 4.13, 4.14, 4.15, 5.14. Formulations clarified: 2.10, 2.11 (former 2.9, 2.10), 3.17, 5.14, 5.15, 5.23. Clarifications/copyedit: remarks 2.11 (former 2.10), 5.17; pages 5, 11, 15, 21, 22, 36, 39, 40, 41, 42; refs [5], [6].