How does the supercritical GMC converge?

Federico Bertacco; Martin Hairer

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arXiv · 2504.06956

How does the supercritical GMC converge?

Federico Bertacco·Martin Hairer

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Abstract

In the spirit of [M. Biskup & O. Louidor, Adv. Math. 330 (2018)], we study the local structure of $\star$-scale invariant fields -- a class of log-correlated Gaussian fields -- around their extremal points by characterising the law of the "shape" of the field's configuration near such points. As a consequence, we obtain a refined understanding of the freezing phenomenon in supercritical Gaussian multiplicative chaos.

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Federico Bertacco, Martin Hairer. 2025-04-09. How does the supercritical GMC converge?. https://arxiv.org/abs/2504.06956

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