Linear response and moderate deviations: hierarchical approach. V

2019/09/07 by Tsirelson, Boris
#Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1909.03238

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 = ψ(G_t) obtained from a Gaussian random field G_t via a function ψ, 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].

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