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January 2018 Lattice approximation to the dynamical $\Phi_{3}^{4}$ model
Rongchan Zhu, Xiangchan Zhu
Ann. Probab. 46(1): 397-455 (January 2018). DOI: 10.1214/17-AOP1188


We study the lattice approximations to the dynamical $\Phi^{4}_{3}$ model by paracontrolled distributions proposed in [Forum Math. Pi 3 (2015) e6]. We prove that the solutions to the lattice systems converge to the solution to the dynamical $\Phi_{3}^{4}$ model in probability, locally uniformly in time. Since the dynamical $\Phi_{3}^{4}$ model is not well defined in the classical sense and renormalisation has to be performed in order to define the nonlinear term, a corresponding suitable drift term is added in the stochastic equations for the lattice systems.


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Rongchan Zhu. Xiangchan Zhu. "Lattice approximation to the dynamical $\Phi_{3}^{4}$ model." Ann. Probab. 46 (1) 397 - 455, January 2018.


Received: 1 October 2015; Revised: 1 February 2017; Published: January 2018
First available in Project Euclid: 5 February 2018

zbMATH: 06865126
MathSciNet: MR3758734
Digital Object Identifier: 10.1214/17-AOP1188

Primary: 60H15 , 82C28

Keywords: $\Phi_{3}^{4}$ model , Paracontrolled distribution , regularity structure , renormalisation , space–time white noise

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.46 • No. 1 • January 2018
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