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arXiv · 2602.14996

Invariant Gibbs dynamics for the hyperbolic sinh-Gordon model

Justin Forlano·Younes Zine
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Abstract

We study the hyperbolic defocusing sinh-Gordon model with parameter $\beta^2>0$ and its associated Gibbs dynamics on the two-dimensional torus. We establish global well-posedness of the model for a certain range of parameters $\beta^2>0$ with the corresponding Gibbs measure initial data and prove invariance of the Gibbs measure under the flow, thereby resolving a question posed by Oh, Robert, and Wang (2019). Our physical space approach hinges on developing a novel $L^\infty$-based well-posedness theory for wave equations with exponential-type nonlinearities, going beyond the classical $L^2$-based framework. This refinement allows us to fully leverage structural properties of Gaussian multiplicative chaos. As a by-product of our method, we also obtain an improved well-posedness theory for the hyperbolic Liouville model.

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Justin Forlano, Younes Zine. 2026-02-16. Invariant Gibbs dynamics for the hyperbolic sinh-Gordon model. https://arxiv.org/abs/2602.14996

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