Wave turbulence and anomalous diffusion in the QGP

High energy QCD jets provide a versatile multi-dimensional tool for probing the properties of the quark-gluon plasma (QGP) produced in ultra relativistic heavy ion collisions at RHIC and LHC. The multiple interactions jets undergo in the QGP cause them to lose energy and alter their substructure. I will discuss the nature of these modifications and how they shed light on the approach to thermal equilibrium of hot QCD matter and thus, on the initial conditions of the QGP formation. I will in particular report on recently uncovered phenomena that emerge as a result of the underlying radiative processes which range from the TeV to the MeV scales such as: color decoherence, turbulent radiative energy loss and anomalous diffusion in QCD matter.