Electronic Journal of Probability

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

Rongchan Zhu and Xiangchan Zhu

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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
Received: 1 July 2017
Accepted: 26 July 2018
First available in Project Euclid: 12 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1536717737

Digital Object Identifier
doi:10.1214/18-EJP207

Mathematical Reviews number (MathSciNet)
MR3858906

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 82C28: Dynamic renormalization group methods [See also 81T17]

Keywords
$\Phi _3^4$ model Dirichlet form paracontrolled distributions regularity structures space-time white noise renormalisation

Rights
Creative Commons Attribution 4.0 International License.

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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