Maximum and coupling of the sine-Gordon field

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.

Accepted version, to appear in Annals of Probability

References in corpus (2)

• Maximum of the integer-valued Gaussian free field
• Another probabilistic construction of ${\Phi }^{2n}$ in dimension 2

Cited by in corpus (3)

• The Coleman correspondence at the free fermion point
• Stochastic dynamics and the Polchinski equation: an introduction
• Multiscale coupling and the maximum of $\mathcal{P}(\varphi {)}_2$ models on the torus