Publication

The density of imaginary multiplicative chaos is positive

Juhan Aru, Antoine Pierre François Jego
2024
Journal Articles

Abstract

Consider a log-correlated Gaussian field Γ and its associated imaginary multiplicative chaos: eiβΓ: where β is a real parameter. In [3], we showed that for any nonzero test function f, the law of∫ f: eiβΓ: possesses a smooth density with respect to Lebesgue measure on C. In this note, we show that this density is strictly positive everywhere on C. Our simple and direct strategy could be useful for studying other functionals on Gaussian spaces.

Official source

https://infoscience.epfl.ch/entities/publication/7655da76-b8fc-4113-9e67-cca4b085d1c9

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