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A simple construction of the sine-Gordon model via stochastic quantization

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arxiv 2412.16404 v1 pith:N7JADR74 submitted 2024-12-20 math.PR math-phmath.APmath.MP

Massimiliano Gubinelli , Martin Hairer , Tadahiro Oh , Younes Zine This is my paper · ORCID
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abstract

We present a simple PDE construction of the sine-Gordon measure below the first threshold ($\be^2 < 4\pi$), in both the finite and infinite volume settings, by studying the corresponding parabolic sine-Gordon model. We also establish pathwise global well-posedness of the hyperbolic sine-Gordon model in finite volume for $\be^2 < 2\pi$.

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  1. Invariant Gibbs measures for the one-dimensional quintic nonlinear Schr\"odinger equation in infinite volume

    math.AP 2025-05 accept novelty 7.0 of 10

    The defocusing quintic NLS on the real line has an invariant infinite-volume Gibbs measure for p between 3 and 5.

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