Invariant Gibbs dynamics for the dynamical sine-Gordon model

Tadahiro Oh, Tristan Robert, Philippe Sosoe, Yuzhao Wang

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

In this note, we study the hyperbolic stochastic damped sine-Gordon equation (SdSG), with a parameter β2 > 0, and its associated Gibbs dynamics on the two-dimensional torus. After introducing a suitable renormalization, we first construct the Gibbs measure in the range 0 < β2 < 4π via the variational approach due to Barashkov-Gubinelli (2018). We then prove almost sure global well-posedness and invariance of the Gibbs measure under the hyperbolic SdSG dynamics in the range 0 < β2 < 2π. Our construction of the Gibbs measure also yields almost sure global well-posedness and invariance of the Gibbs measure for the parabolic sine-Gordon model in the range 0 < β2 < 4π.

Original languageEnglish
Pages (from-to)1450-1466
Number of pages17
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume151
Issue number5
Early online date16 Sept 2020
DOIs
Publication statusPublished - Oct 2021

Bibliographical note

Publisher Copyright:
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.

Keywords

  • dynamical sine-Gordon model
  • Gaussian multiplicative chaos
  • Gibbs measure
  • renormalization
  • Stochastic sine-Gordon equation
  • white noise

ASJC Scopus subject areas

  • General Mathematics

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