We study the density field around zem > 4 quasars using high-quality medium spectral resolution Echelle Spectrograph and Imager-Keck spectra (R∼ 4300, signal-to-noise ratio (S/N) > 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 photoionization 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 photoionization 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 h-1 Mpc. The mean overdensity is of the order of 2 and 5 within, respectively, 10 and 3 h-1 Mpc. If true, this would indicate that high-redshift quasars are located in the centre of overdense regions that could evolve with time into massive clusters of galaxies. The overdensity is correlated with luminosity: brighter quasars show higher overdensities
