  We study the density field around z_em > 4 quasars using high quality medium
spectral resolution ESI-Keck spectra (R~4300, SNR > 25) of 45 high-redshift
quasars selected from a total of 95 spectra. This large sample considerably
increases the statistics compared to previous studies. The redshift evolution
of the mean photo-ionization rate and the median optical depth of the
intergalactic medium (IGM) are derived statistically from the observed
transmitted flux and the pixel optical depth probability distribution function
respectively. This is used to study the so-called proximity effect, that is,
the observed decrease of the median optical depth of the IGM in the vicinity of
the quasar caused by enhanced photo-ionization rate due to photons emitted by
the quasar. We show that the proximity effect is correlated with the luminosity
of the quasars, as expected. By comparing the observed decrease of the median
optical depth with the theoretical expectation we find that the optical depth
does not decrease as rapidly as expected when approaching the quasar if the gas
in its vicinity is part of the standard IGM. We interpret this effect as
revealing gaseous overdensities on scales as large as ~15 Mpc/h. The mean
overdensity is of the order of two and five within, respectively, 10 and 3
Mpc/h. If true, this would indicate that high redshift quasars are located in
the center of overdense regions that could evolve with time into massive
clusters of galaxies. The overdensity is correlated with luminosity: brighter
quasars show higher overdensities.
