Title:Moderate deviations for random fields and random complex zeroes

Abstract:
Recent results on moderate deviations for random complex zeroes [Nazarov, Sodin, Volberg - arXiv:0707.3863] are a 
challenge for probability theory, since they involve complex analysis, in contrast to asymptotic normality obtained 
via random fields [Sodin, Tsirelson - arXiv:math.CV/0210090]. Taking up the challenge, I deduce moderate deviations 
for random complex zeroes from a new general theorem on moderate deviations for random fields. As a by-product, the 
same general theorem gives the asymptotic normality, avoiding the diagram techniques of [Sodin, Tsirelson]. (See also 
[Tsirelson - arXiv:0801.1050].)