Linear response and moderate deviations: hierarchical approach. V

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].