Linear response and moderate deviations: hierarchical approach. II

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. An upper bound for a new class of random fields is obtained here by induction in dimension. Version 3. Sect 1. Stationarity, being not essential in the proofs, is removed from the definitions and the main result formulation. Sect. 2. $[C,2C]$ instead of $[C_1,2C_1]$ before Prop. 2.6; $ a\ge1$ instead of $a\ge C/C_1$ in the last proof; Remark 2.5 added; supremum over shifts in (2.2) (formerly (2.3)); "centered" instead of "CMS". Cosmetic changes: indexing of leaks; Remark 2.11. Sect. 3. Cosmetic change: semicolon after the second display of the proof of Lemma 3.9. References: "response", not "responce".