Lattice approximation to the dynamical $\Phi_3^4$ model
Probability
2015-08-25 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We study the lattice approximations to the dynamical model by paracontrolled distributions proposed in [GIP13]. We prove that the solutions to the lattice systems converge to the solution to the dynamical model in probability, locally in time. The dynamical model is not well defined in the classical sense. Renormalisation has to be performed in order to define the non-linear term. Formally, this renormalisation corresponds to adding an infinite mass term to the equation which leads to adding a drift term in the lattice systems.
Cite
@article{arxiv.1508.05613,
title = {Lattice approximation to the dynamical $\Phi_3^4$ model},
author = {Rongchan Zhu and Xiangchan Zhu},
journal= {arXiv preprint arXiv:1508.05613},
year = {2015}
}