Dirichlet form associated with the $\Phi_3^4$ model
Probability
2017-06-27 v2 Analysis of PDEs
Functional Analysis
Abstract
We construct the Dirichlet form associated with the dynamical model obtained in [Hai14, CC13] and [MW16]. 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 field measure as an invariant (even symmetrizing) measure.
Cite
@article{arxiv.1703.09987,
title = {Dirichlet form associated with the $\Phi_3^4$ model},
author = {Rongchan Zhu and Xiangchan Zhu},
journal= {arXiv preprint arXiv:1703.09987},
year = {2017}
}