Abstract
In this article, we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos.
We prove two decomposition theorems. The first one is a global one and says that if the difference between the covariance kernels of two Gaussian fields, taking values in some Sobolev space, has suitable Sobolev regularity, then these fields differ by a Hölder continuous Gaussian process. Our second decomposition theorem is more specialized and is in the setting of Gaussian fields whose covariance kernel has a logarithmic singularity on the diagonal—or log-correlated Gaussian fields. The theorem states that any log-correlated Gaussian field
We use these decompositions to extend several results that have been known basically only for
Citation
Janne Junnila. Eero Saksman. Christian Webb. "Decompositions of log-correlated fields with applications." Ann. Appl. Probab. 29 (6) 3786 - 3820, December 2019. https://doi.org/10.1214/19-AAP1492
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