  We study the color randomization of two-gluon states produced after splitting
of a primary fast gluon in the quark-gluon plasma. We find that for the LHC
conditions the color randomization of the $gg$ pairs is rather slow. At jet
energies $E=100$ and $500$ GeV, for typical jet path length in the plasma in
central Pb+Pb collisions, the $SU(3)$-multiplet averaged color Casimir of the
$gg$ pair differs considerably from its value $2N_c$ for a fully randomized
$gg$ state. Our calculations of the energy dependence for generation of the
nearly collinear decuplet $gg$ states, that can lead to the baryon jet
fragmentation, show that the contribution of the anomalous decuplet color
states to the baryon production should become small at $p_T\gtrsim 10$ GeV.
