We discuss the evolution of an energetic jet which propagates through a dense quark-gluon plasma
and radiates gluons due to its interactions with the medium. Within perturbative QCD,
this evolution can be described as a stochastic branching process, that we have managed to solve exactly.
We present exact, analytic, results for the gluon spectrum (the average gluon distribution)
and for the higher n-point functions, which describe correlations and fluctuations.
Using these results, we construct the event-by-event picture of the gluon distribution produced via medium-induced gluon branching.
In contrast to what happens in a usual QCD cascade
in vacuum, the medium-induced branchings are quasi-democratic, with offspring gluons carrying sizable fractions of the energy of their parent parton. This results in wave turbulence -
an efficient mechanism for the transport of energy from the jet towards the medium.
This mechanism is characterized by a power-law (Kolmogorov) spectrum
and by large fluctuations in the energy loss and the multiplicity
of soft gluons. The multiplicity distribution is predicted to
exhibit KNO (Koba-Nielsen-Olesen) scaling. These predictions can be tested
in Pb+Pb collisions at the LHC, via event-by-event measurements of the di-jet asymmetry.
Based on e-Print: arXiv:1601.03629 [hep-ph] published in JHEP 1605 (2016) 008