Thermalization of the quark gluon plasma in heavy ion collisions is an open problem that has given rise to many works in recent years. On the one hand, viscous hydrodynamics simulations suggest that the matter produced in such collisions (called the Quark Gluon Plasma, or QGP) behaves like a nearly perfect fluid. Since hydrodynamic models require local thermal equilibrium, this tends to show that the QGP has thermalized very shortly after the collision (around 1 fm/c). On the other hand, theoretical models predict that the QGP is very far from local thermal equilibrium at the initial time (its energy-momentum is very anisotropic).
One of the approaches developed to study this non-perturbative problem in QCD is a resummation scheme that amounts to averaging over classical fields, with random initial conditions. Its numerical implementation is presented here for the case of a scalar field theory with quartic coupling, that shares some important features with QCD (scale invariance at the classical level and the presence of instabilities). In particular, we will show the relevance of this resummation in capturing the physics relevant for thermalization.