GLOBAL WELL-POSEDNESS OF THE DYNAMICAL SINE-GORDON MODEL UP TO 6π

BJOERN BRINGMANN; SKY CAO

doi:10.1214/25-AOP1797

GLOBAL WELL-POSEDNESS OF THE DYNAMICAL SINE-GORDON MODEL UP TO 6π

BJOERN BRINGMANN
, SKY CAO

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the global well-posedness of the dynamical sine-Gordon model up to the third threshold, that is, for parameters β² < 6π. The key novelty in our approach is the introduction of the so-called resonant equation, whose solution is entirely deterministic and completely captures the size of the solution to the dynamical sine-Gordon model. The probabilistic fluctuations in the dynamical sine-Gordon model are then controlled using uniform estimates for modified stochastic objects.

Original language	English (US)
Pages (from-to)	1564-1607
Number of pages	44
Journal	Annals of Probability
Volume	54
Issue number	3
DOIs	https://doi.org/10.1214/25-AOP1797
State	Published - Jan 2026

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Abelian-Higgs
Gibbs measures
Global well-posedness
singular SPDEs
Yang-Mills

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10.1214/25-AOP1797

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abstract = "We prove the global well-posedness of the dynamical sine-Gordon model up to the third threshold, that is, for parameters β2 < 6π. The key novelty in our approach is the introduction of the so-called resonant equation, whose solution is entirely deterministic and completely captures the size of the solution to the dynamical sine-Gordon model. The probabilistic fluctuations in the dynamical sine-Gordon model are then controlled using uniform estimates for modified stochastic objects.",

keywords = "Abelian-Higgs, Gibbs measures, Global well-posedness, singular SPDEs, Yang-Mills",

author = "BJOERN BRINGMANN and SKY CAO",

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AB - We prove the global well-posedness of the dynamical sine-Gordon model up to the third threshold, that is, for parameters β2 < 6π. The key novelty in our approach is the introduction of the so-called resonant equation, whose solution is entirely deterministic and completely captures the size of the solution to the dynamical sine-Gordon model. The probabilistic fluctuations in the dynamical sine-Gordon model are then controlled using uniform estimates for modified stochastic objects.

KW - Abelian-Higgs

KW - Gibbs measures

KW - Global well-posedness

KW - singular SPDEs

KW - Yang-Mills

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GLOBAL WELL-POSEDNESS OF THE DYNAMICAL SINE-GORDON MODEL UP TO 6π

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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