Lattice approximation to the dynamical $\Phi_3^4$ model
Abstract
We study the lattice approximations to the dynamical $\Phi^4_3$ model by paracontrolled distributions proposed in [GIP13]. We prove that the solutions to the lattice systems converge to the solution to the dynamical $\Phi_3^4$ model in probability, locally in time. The dynamical $\Phi_3^4$ model is not well defined in the classical sense. Renormalisation has to be performed in order to define the nonlinear 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2015
 arXiv:
 arXiv:1508.05613
 Bibcode:
 2015arXiv150805613Z
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Analysis of PDEs