MAXIMUM AND COUPLING OF THE SINE-GORDON FIELD
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Authors
Bauerschmidt, R
Hofstetter, M
Publication Date
2022Journal Title
Annals of Probability
ISSN
0091-1798
Publisher
Institute of Mathematical Statistics
Type
Article
This Version
AM
Metadata
Show full item recordCitation
Bauerschmidt, R., & Hofstetter, M. (2022). MAXIMUM AND COUPLING OF THE SINE-GORDON FIELD. Annals of Probability https://doi.org/10.1214/21-AOP1537
Abstract
For $0<\beta<6\pi$, we prove that the distribution of the centred maximum of
the $\epsilon$-regularised continuum sine-Gordon field on the two-dimensional
torus converges to a randomly shifted Gumbel distribution as $\epsilon \to 0$.
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
math.PR, math.PR, math-ph, math.MP
Identifiers
External DOI: https://doi.org/10.1214/21-AOP1537
This record's URL: https://www.repository.cam.ac.uk/handle/1810/333726
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