TL;DR
This paper introduces a new definition and approach for Gaussian multiplicative chaos (GMC), establishing general uniqueness and convergence results for subcritical GMC across various Gaussian fields.
Contribution
It presents a novel definition of GMC and links subcritical GMC to Gaussian measure shifts, enabling broad applicability and rigorous results.
Findings
Established a new definition for GMC
Proved general uniqueness and convergence results
Applicable to Gaussian fields with arbitrary covariance kernels
Abstract
We propose a new definition of the Gaussian multiplicative chaos (GMC) and an approach based on the relation of subcritical GMC to randomized shifts of a Gaussian measure. Using this relation we prove general uniqueness and convergence results for subcritical GMC that hold for Gaussian fields with arbitrary covariance kernels.
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