Dirichlet form associated with the Φ4 3 model

Rongchan Zhu, Xiangchan Zhuï*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We construct the Dirichlet form associated with the dynamical Φ4 3 model obtained in [23, 7] and [37]. This Dirichlet form on cylinder functions is identified as a classical gradient bilinear form. As a consequence, this classical gradient bilinear form is closable and then by a well-known result its closure is also a quasi-regular Dirichlet form, which means that there exists another (Markov) diffusion process, which also admits the Φ4 3 field measure as an invariant (even symmetrizing) measure.

Original languageEnglish
Article number78
JournalElectronic Journal of Probability
Volume23
DOIs
Publication statusPublished - 2018

Keywords

  • Dirichlet form
  • Paracontrolled distributions
  • Regularity structures
  • Renormalisation
  • Space-time white noise
  • Φ model

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