  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. We find large fluctuations in the energy loss
and in 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 JHEP 1605 (2016) 008 and arXiv:1609.06104
