  When hadrons scatter at high energies, strong color fields, whose dynamics is
described by quantum chromodynamics (QCD), are generated at the interaction
point. If one represents these fields in terms of partons (quarks and gluons),
the average number densities of the latter saturate at ultrahigh energies. At
that point, nonlinear effects become predominant in the dynamical equations.
The hadronic states that one gets in this regime of QCD are generically called
"color glass condensates".
  Our understanding of scattering in QCD has benefited from recent progress in
statistical and mathematical physics. The evolution of hadronic scattering
amplitudes at fixed impact parameter in the regime where nonlinear parton
saturation effects become sizable was shown to be similar to the time evolution
of a system of classical particles undergoing reaction-diffusion processes. The
dynamics of such a system is essentially governed by equations in the
universality class of the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov
equation, which is a stochastic nonlinear partial differential equation.
Realizations of that kind of equations (that is, "events" in a particle physics
language) have the form of noisy traveling waves. Universal properties of the
latter can be taken over to scattering amplitudes in QCD.
  This review provides an introduction to the basic methods of statistical
physics useful in QCD, and summarizes the correspondence between these two
fields and its theoretical and phenomenological implications.
