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Uniqueness of supercritical Gaussian multiplicative chaos (2504.07552v2)
Published 10 Apr 2025 in math.PR, math-ph, and math.MP
Abstract: We show that, for general convolution approximations to a large class of log-correlated Gaussian fields, the properly normalised supercritical Gaussian multiplicative chaos measures converge stably to a nontrivial limit. This limit depends on the choice of regularisation only through a multiplicative constant and can be characterised as an integrated atomic measure with a random intensity expressed in terms of the critical Gaussian multiplicative chaos.
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