Abstract
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.
Original language | English (US) |
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Pages (from-to) | 455-508 |
Number of pages | 54 |
Journal | Annals of Probability |
Volume | 50 |
Issue number | 2 |
DOIs | |
State | Published - Mar 2022 |
Keywords
- Gaussian free field
- Maximum
- coupling
- sine-Gordon field
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty