Finding the high-energy limit of QCD is a longstanding problem. It has been shown in the past decade that saturation effects are of prime importance in that limit. After a brief overview of the evolution equation including these effects, I shall show how an analogy with well-studied problems in statistical mechanics allows us to find asymptotic solutions for the equations of QCD. I shall explain how, in the cas of the impact-parameter-independent equation, this lead to the formation of traveling waves and geometric scaling. I shall then extend this to the case of the full equation, including all phase-space dependence. In the last part of the talk, I shall consider the effects of the recently-introduced fluctuations. In particular, I shall concentrate on their effects on asymptotic solutions and geometric scaling.

SPhT, CEA/Saclay