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Abstract |
In this talk I will talk about the lattice approximations to the dynamical $\Phi^4_3$ model by paracontrolled distributions. 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 non-linear term, a corresponding suitable drift term is added in the stochastic equations for the lattice systems. Moreover, this can be applied to the construction of the Dirichlet form associated with the dynamical $\Phi^4_3$ model. |
