Abstract
In the present paper, we show that (under some minor technical assumption) Complex Gaussian multiplicative chaos defined as the complex exponential of a log-correlated Gaussian field can be obtained by taking the limit of the exponential of the field convoluted with a smoothing kernel. We consider two types of chaos: for a log correlated field X and , and for X and Y two independent fields with . Our result is valid in the range
which, up to boundary, is conjectured to be optimal.
Funding Statement
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 837793.
Acknowledgment
The author is grateful to Nathanaël Berestycki, R. Rhodes and Christian Webb for their feedback on a first version of this manuscript. He also wishes to thank the anonymous referee for numerous helpful comments and observation. This work has been realized in part during the author’s stay in Aix Marseille University as a MSCA fellow. He acknowledges kind hospitality and support.
Citation
Hubert Lacoin. "A universality result for subcritical complex Gaussian multiplicative chaos." Ann. Appl. Probab. 32 (1) 269 - 293, February 2022. https://doi.org/10.1214/21-AAP1677
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