  Observational constraints on the average radial distribution profile of AGN
in distant galaxy clusters can provide important clues on the triggering
mechanisms of AGN activity in dense environments and are essential for a
completeness evaluation of cluster selection techniques in the X-ray and
mm-wavebands. The aim of this work is a statistical study with XMM-Newton of
the presence and distribution of X-ray AGN in the large-scale structure
environments of 22 X-ray luminous galaxy clusters in the redshift range 0.9 < z
\lesssim 1.6 compiled by the XMM-Newton Distant Cluster Project (XDCP). To this
end, the X-ray point source lists from detections in the soft-band (0.35-2.4
keV) and full-band (0.3-7.5 keV) were stacked in cluster-centric coordinates
and compared to average background number counts extracted from three
independent control fields in the same observations. A significant full-band
(soft-band) excess of \sim78 (67) X-ray point sources is found in the cluster
fields within an angular distance of 8' (4Mpc) at a statistical confidence
level of 4.0 sigma (4.2 sigma), corresponding to an average number of detected
excess AGN per cluster environment of 3.5\pm0.9 (3.0\pm0.7). The data point
towards a rising radial profile in the cluster region (r<1Mpc) of predominantly
low-luminosity AGN with an average detected excess of about one point source
per system, with a tentative preferred occurrence along the main cluster
elongation axis. A second statistically significant overdensity of brighter
soft-band detected AGN is found at cluster-centric distances of 4'-6' (2-3Mpc),
corresponding to about three times the average cluster radius R200 of the
systems. If confirmed, these results would support the idea of two different
physical triggering mechanisms of X-ray AGN activity in dependence of the
radially changing large-scale structure environment of the distant clusters.
