On the two-dimensional hyperbolic stochastic sine-Gordon equation

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External organisations

  • University of Edinburgh
  • Bielefeld University
  • Cornell University


We study the two-dimensional stochastic sine-Gordon equation (SSG) in the hyperbolic setting. In particular, by introducing a suitable time-dependent renormalization for the relevant imaginary Gaussian multiplicative chaos, we prove local well-posedness of SSG for any value of a parameter β2>0 in the nonlinearity. This exhibits sharp contrast with the parabolic case studied by Hairer and Shen (Commun Math Phys 341(3):933–989, 2016) and Chandra et al. (The dynamical sine-Gordon model in the full subcritical regime, arXiv:1808.02594 [math.PR], 2018), where the parameter is restricted to the subcritical range: 0<β2<8π. We also present a triviality result for the unrenormalized SSG.


Original languageEnglish
Number of pages32
JournalStochastics and Partial Differential Equations: Analysis and Computations
Publication statusPublished - 5 Feb 2020


  • stochastic sine-Gordon equation, sine-Gordon equation, renormalization, white noise, Gaussian multiplicative chaos