  The X-ray variability of the Active Galactic Nuclei (AGN) has been most often
investigated with studies of individual, nearby, sources, and only a few
ensemble analyses have been applied to large samples in wide ranges of
luminosity and redshift. We want to determine the ensemble variability
properties of two serendipitously selected AGN samples extracted from the
catalogues of XMM-Newton and Swift, with redshift between ~0.2 and ~4.5, and
X-ray luminosities, in the 0.5-4.5 keV band, between ~10^43 erg/s and ~10^46
erg/s. We use the structure function (SF), which operates in the time domain,
and allows for an ensemble analysis even when only a few observations are
available for individual sources and the power spectral density (PSD) cannot be
derived. SF is also more appropriate than fractional variability and excess
variance, because such parameters are biased by the duration of the monitoring
time interval in the rest-frame, and thus by cosmological time dilation. We
find statistically consistent results for the two samples, with the SF
described by a power law of the time lag, approximately as SF \propto tau^0.1.
We do not find evidence of the break in the SF, at variance with the case of
lower luminosity AGNs. We confirm a strong anti-correlation of the variability
with X-ray luminosity, accompanied by a change of the slope of the SF. We find
evidence in support of a weak, intrinsic, average increase of X-ray variability
with redshift. The change of amplitude and slope of the SF with X-ray
luminosity provides new constraints on both single oscillator models and
multiple subunits models of variability.
