Random walks of partons inSU(Nc)and classical representations of color charges in QCD at smallx

The effective action for wee partons in large nuclei includes a sum over static color sources distributed in a wide range of representations of the $\mathrm{S}\mathrm{U}(N_c)$ color group. The problem can be formulated as a random walk of partons in the $N_c-1$ dimensional space of the Casimir operators of $\mathrm{S}\mathrm{U}(N_c)$. For a large number of sources, $k\gg 1$, we show explicitly that the most likely representation is a classical representation of order $O(\sqrt{k})$. The quantum sum over representations is well approximated by a path integral over classical sources with an exponential weight whose argument is the quadratic Casimir operator of the group. The contributions of the higher $N_c-2$ Casimir operators are suppressed by powers of $k$. Other applications of the techniques developed here are discussed briefly.