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MAXIMUM AND COUPLING OF THE SINE-GORDON FIELD

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Bauerschmidt, Roland  ORCID logo  https://orcid.org/0000-0001-7453-2737
Hofstetter, M 

Abstract

For 0<β<6π, we prove that the distribution of the centred maximum of the ϵ-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.

Description

Keywords

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

Journal Title

Annals of Probability

Conference Name

Journal ISSN

0091-1798
2168-894X

Volume Title

Publisher

Institute of Mathematical Statistics