[en] In the context of the recently derived probabilistic picture of in-medium jet evolution, we study radiative corrections which yield potentially large double logarithms, α_s ln² L, for large enough medium length L. We show that these large corrections are universal and can be reabsorbed in a renormalization of the jet quenching parameter controlling both momentum broadening and energy loss. The renormalized jet-quenching parameter is enhanced compared to its standard perturbative estimate. As a particular consequence, the radiative energy loss scales with medium size L as L^2+γ, with γ = $\sqrt{{\mathrm{\alpha <!--\; ??\; -->}}_s{N}_c/\mathrm{\pi <!--\; ??\; -->}}$, as compared to the standard scaling in L². (paper)