  This is the third paper of a series describing the Asiago-ESO/RASS QSO survey
(AERQS), a project aimed at the construction of an all-sky statistically
well-defined sample of relatively bright QSOs (B<15) at z<0.3. We present here
the clustering analysis of the full spectroscopically identified database (392
AGN). The clustering signal at 0.02<z<0.22 is detected at a 3-4 sigma level and
its amplitude is measured to be r_0=8.6\pm 2.0 h^{-1} Mpc (in a LambdaCDM
model). The comparison with other classes of objects shows that low-redshift
QSOs are clustered in a similar way to Radio Galaxies, EROs and early-type
galaxies in general, although with a marginally smaller amplitude. The
comparison with recent results from the 2QZ shows that the correlation function
of QSOs is constant in redshift or marginally increasing toward low redshift.
We discuss this behavior with physically motivated models, deriving interesting
constraints on the typical mass of the dark matter halos hosting QSOs, M_DMH=
10^{12.7} h^{-1} M_sun (10^{12.0}-10^{13.5}h^{-1} M_sun at 1 sigma confidence
level). Finally, we use the clustering data to infer the physical properties of
local AGN, obtaining M_BH=2 10^8 h^{-1} M_sun (10^7-3 10^9 h^{-1} M_sun) for
the mass of the active black holes, tau_{AGN}= 8 10^6 yr (2 10^{6}-5 10^{7} yr)
for their life-time and eta = 0.14 for their efficiency (always for a LambdaCDM
model).
