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arXiv · 2009.09664

Maximum and coupling of the sine-Gordon field

Roland Bauerschmidt·Michael Hofstetter
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Abstract

For $0<\beta<6\pi$, we prove that the distribution of the centred maximum of the $\epsilon$-regularised continuum sine-Gordon field on the two-dimensional torus converges to a randomly shifted Gumbel distribution as $\epsilon \to 0$. Our proof relies on a strong coupling at all scales of the sine-Gordon field with the Gaussian free field, of independent interest, and extensions of existing methods for the maximum of the lattice Gaussian free field.

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Roland Bauerschmidt, Michael Hofstetter. 2020-09-21. Maximum and coupling of the sine-Gordon field. https://doi.org/10.1214/21-aop1537

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