Cross-fertilization of QCD and statistical physics: High energy scattering, reaction-diffusion, selective evolution, spin glasses and their connections

High energy scattering was recently shown to be similar to a reaction- diffusion process. The latter defines a wide universality class that also contains e.g. some specific population evolution models. The common point of all these models is that their respective dynamics are described by noisy traveling wave equations. This observation has led to a new understanding of QCD in the regime of high energies, and known universal results on reaction-diffusion models could be transposed to obtain quantitative properties of QCD amplitudes. Conversely, new general results for that kind of statistical models have also been derived. Furthermore, an intriguing relationship between noisy traveling wave equations and the theory of spin glasses was found.