MAXIMUM AND COUPLING OF THE SINE-GORDON FIELD

Roland Bauerschmidt, Michael Hofstetter

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)455-508
Number of pages54
JournalAnnals of Probability
Volume50
Issue number2
DOIs
StatePublished - Mar 2022

Keywords

  • Gaussian free field
  • Maximum
  • coupling
  • sine-Gordon field

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint

Dive into the research topics of 'MAXIMUM AND COUPLING OF THE SINE-GORDON FIELD'. Together they form a unique fingerprint.

Cite this