@article{bb9ac4d0ffcc4e98a9a57514a14896ec,
title = "MAXIMUM AND COUPLING OF THE SINE-GORDON FIELD",
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.",
keywords = "Gaussian free field, Maximum, coupling, sine-Gordon field",
author = "Roland Bauerschmidt and Michael Hofstetter",
note = "Funding Information: Funding. RB gratefully acknowledges funding from the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (Grant Agreement No. 851682 SPINRG). MH was partially supported by the UK EPSRC Grant EP/L016516/1 for the Cambridge Centre for Analysis. Funding Information: RB gratefully acknowledges funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No. 851682 SPINRG). MH was partially supported by the UK EPSRC Grant EP/L016516/1 for the Cambridge Centre for Analysis. Publisher Copyright: {\textcopyright} 2022 Institute of Mathematical Statistics. All Rights Reserved.",
year = "2022",
month = mar,
doi = "10.1214/21-AOP1537",
language = "English (US)",
volume = "50",
pages = "455--508",
journal = "Annals of Probability",
issn = "0091-1798",
publisher = "Institute of Mathematical Statistics",
number = "2",
}