Invariant Gibbs measures for the 2-d defocusing nonlinear wave equations

Tadahiro Oh, Laurent Thomann

Research output: Contribution to journalArticlepeer-review


We consider the defocusing nonlinear wave equations (NLW) on the two-dimensional torus. In particular, we construct invariant Gibbs measures for the renormalized so-called Wick ordered NLW. We then prove weak universality of the Wick ordered NLW, showing that the Wick ordered NLW naturally appears as a suitable scaling limit of non-renormalized NLW with Gaussian random initial data.
Original languageEnglish
Number of pages21
JournalAnnales de la Faculte des Sciences de Toulouse
Issue number1
Publication statusPublished - 24 Jul 2020


  • nonlinear wave equation
  • nonlinear Klein-Gordon equation
  • Gibbs measure
  • Wick ordering
  • Hermite polynomial
  • white noise functional
  • weak universality


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