The primordial environment of super massive black holes: large scale
  galaxy overdensities around $z\sim6$ QSOs with LBT
  We investigated the presence of galaxy overdensities around four $z\sim6$
QSOs, namely SDSS J1030+0524 (z = 6.28), SDSS J1148+5251 (z = 6.41), SDSS
J1048+4637 (z = 6.20) and SDSS J1411+1217 (z = 5.95), through deep $r$-, $i$-
and $z$- band imaging obtained with the wide-field ($\sim23'\times25'$) Large
Binocular Camera (LBC) at the Large Binocular Telescope (LBT). We adopted
color-color selections within the $i-z$ vs $r-z$ plane to identify samples of
$i$-band dropouts at the QSO redshift and measure their relative abundance and
spatial distribution in the four LBC fields, each covering $\sim8\times8$
physical Mpc at $z\sim6$. The same selection criteria were then applied to
$z$-band selected sources in the $\sim$1 deg$^2$ Subaru-XMM Newton Deep Survey
to derive the expected number of dropouts over a blank LBC-sized field
($\sim$0.14 deg$^2$). The four observed QSO fields host a number of candidates
larger than what is expected in a blank field. By defining as $i$-band dropouts
objects with $z_{AB}<25$, $i-z>1.4$ and undetected in the $r$-band, we found
16, 10, 9, 12 dropouts in SDSS J1030+0524, SDSS J1148+5251, SDSS J1048+4637,
and SDSS J1411+1217, respectively, whereas only 4.3 such objects are expected
over a 0.14 deg$^2$ blank field. This corresponds to overdensity significances
of 3.3, 1.9, 1.7, 2.5$\sigma$, respectively. By considering the total number of
dropouts in the four LBC fields and comparing it with what is expected in four
blank fields of 0.14 deg$^2$ each, we find that high-z QSOs reside in overdense
environments at the $3.7\sigma$ level. This is the first direct and unambiguous
measurement of the large scale structures around $z\sim6$ QSOs. [shortened]
