Dirichlet form associated with the $\Phi_3^4$ model

Rongchan Zhu; Xiangchan Zhu

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arXiv · 1703.09987

Dirichlet form associated with the $\Phi_3^4$ model

Rongchan Zhu·Xiangchan Zhu

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Abstract

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

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Rongchan Zhu, Xiangchan Zhu. 2017-03-29. Dirichlet form associated with the $\Phi_3^4$ model. https://arxiv.org/abs/1703.09987

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