  In the first part we study the possibility that a Disoriented Chiral
Condensate (DCC) forms when hot hadronic matter is quenched, using the linear
sigma model. We formulate an original sampling strategy for the initial field
configuration in order to get an estimate of the probability that a potentially
observable coherent pion field appears in a heavy-ion collision. We obtain a
probability of the order of 1/1000 at CERN SPS energies. Next, we study the
correlation between isospin orientations of the distinct modes of the pion
field emerging after a quench. We show that this correlation is absent: the
distinct modes behave as distinct DCCs. This contradicts the common belief that
the state produced in the simplest form of the quench scenario - with a fully
thermalized initial state - is identical to the originally proposed DCC. In the
second part, we investigate the role of elastic scatterings in the process of
kinetic equilibration of gluons produced in the very early times of the
collision. We compare the two available scenarios describing the initial
conditions: saturation and minijet production. We treat the elastic processes
in the small scattering angle limit and work in the relaxation time
approximation. By measuring the isotropy of different observables as a function
of time, we show that the usual assumption that elastic collisions are
efficient enough to rapidly achieve kinetic equilibrium is not reliable. Due to
the longitudinal expansion at early times, the actual equilibration time is an
order of magnitude bigger than the typical 1 fm estimate usually assumed.
