## Electronic Journal of Probability

### Dirichlet form associated with the $\Phi _3^4$ model

#### Abstract

We construct the Dirichlet form associated with the dynamical $\Phi ^4_3$ 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 $\Phi ^4_3$ ﬁeld measure as an invariant (even symmetrizing) measure.

#### Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 78, 31 pp.

Dates
Accepted: 26 July 2018
First available in Project Euclid: 12 September 2018

https://projecteuclid.org/euclid.ejp/1536717737

Digital Object Identifier
doi:10.1214/18-EJP207

Mathematical Reviews number (MathSciNet)
MR3858906

#### Citation

Zhu, Rongchan; Zhu, Xiangchan. Dirichlet form associated with the $\Phi _3^4$ model. Electron. J. Probab. 23 (2018), paper no. 78, 31 pp. doi:10.1214/18-EJP207. https://projecteuclid.org/euclid.ejp/1536717737

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