  We study the spatial distribution of X-ray selected AGN in the framework of
hierarchical co-evolution of supermassive black holes and their host galaxies
and dark matter haloes. To this end, we have applied the model developed by
Croton et al.(2006), De Lucia & Blaizot(2007) and Marulli et al.(2008) to the
output of the Millennium Run and obtained hundreds of realizations of past
light-cones from which we have extracted realistic mock AGN catalogues that
mimic the Chandra deep fields. We find that the model AGN number counts are in
fair agreement with observations, except at fluxes <1e-15 erg/cm^2/s. The
spatial two-point correlation function predicted by the model is well described
by a power-law relation out to 20 Mpc/h, in close agreement with observations.
Our model matches the correlation length r_0 of AGN in the Chandra Deep Field
North but underestimates it in the Chandra Deep Field South. When fixing the
slope to gamma = 1.4, as in Gilli et al. (2005), the statistical significance
of the mismatch is 2-2.5 sigma, suggesting that the predicted cosmic variance,
which dominates the error budget, may not account for the different correlation
length of the AGN in the two fields. While our results are robust to changes in
the model prescriptions for the AGN lightcurves, the luminosity dependence of
the clustering is sensitive to the different lightcurve models adopted.
However, irrespective of the model considered, the luminosity dependence of the
AGN clustering in our mock fields seems to be weaker than in the real Chandra
fields. The significance of this mismatch needs to be confirmed using larger
datasets.
