  We study theoretically the statistical properties of the
Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between localized magnetic
moments in a disordered two-dimensional electron gas with both Rashba and
Dresselhaus spin-orbit couplings. Averaging over disorder, the static spin
susceptibility tensor is evaluated diagrammatically in the mesoscopic
(phase-coherent) regime. The disorder-averaged susceptibility leads to a
twisted exchange interaction suppressed exponentially with distance, whereas
the second-order correlations, which determine the fluctuations (variance) of
the RKKY energy, decay with the same power-law as in the clean case. We obtain
analytic expressions in the limits of large/small spin orbit interactions and
for equal Rashba and Dresselhaus couplings. Beside these limiting cases, we
study numerically the variance of the RKKY interaction in the presence of pure
Rashba spin-orbit coupling. Our results are relevant for magnetic impurities or
nuclear moments embedded in III-V two-dimensional heterostructures or in
contact with surface states of metals and metal alloys, which can display a
sizable Rashba spin-orbit coupling.
