For 0 <β< 6π, we prove that the distribution of the centred maximum of the s-regularised continuum sine-Gordon field on the two-dimensional torus converges to a randomly shifted Gumbel distribution as ε →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.
- Gaussian free field
- sine-Gordon field
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty