  Selective excitation of a diffusive system's transmission eigenchannels
enables manipulation of its internal energy distribution. The fluctuations and
correlations of the eigenchannels' spatial profiles, however, remain unexplored
so far. Here we show that the depth profiles of high-transmission eigenchannels
exhibit low realization-to-realization fluctuations. Furthermore, our
experimental and numerical studies reveal the existence of inter-channel
correlations, which are significant for low-transmission eigenchannels. Because
high-transmission eigenchannels are robust and independent from other
eigenchannels, they can reliably deliver energy deep inside turbid media.
