  We study the local density of states (LDOS) of two-dimensional electrons in
the presence of spin-orbit (SO) coupling. Although SO coupling has no effect on
the average density of states, it manifests itself in the correlations of the
LDOS. Namely, the correlation function acquires two satellites centered at
energy difference equal to the SO splitting, $2\omega_{SO}$, of the electron
Fermi surface. For a smooth disorder the satellites are well separated from the
main peak. Weak Zeeman splitting $\omega_{Z} \ll \omega_{SO}$ in a parallel
magnetic field causes an anomaly in the shape of the satellites. We consider
the effect of SO-induced satellites in the LDOS correlations on the shape of
the correlation function of resonant-tunneling conductances at different
source-drain biases, which can be measured experimentally. This shape is
strongly sensitive to the relation between $\omega_{SO}$ and $\omega_{Z}$.
