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Characterizing high-z quasar environments is key to understanding theco-evolution of quasars and the surrounding galaxies. To restrict their globalpicture, we statistically examine the g-dropout galaxy overdensity distributionaround 570 faint quasar candidates at z ~ 4, based on the Hyper Suprime-CamSubaru Strategic Program survey. We compare the overdensity significances ofg-dropout galaxies around the quasars with those around g-dropout galaxies, andfind no significant difference between their distributions. A total of 4 (22)out of the 570 faint quasars, 0.7_{-0.4}^{+0.4} (3.9_{-0.8}^{+0.8}) %, arefound to be associated with the > 4 sigma overdense regions within an angularseparation of 1.8 (3.0) arcmin, which is the typical size of protoclusters atthis epoch. This is similar to the fraction of g-dropout galaxies associatedwith the > 4 sigma overdense regions. This result is consistent with ourprevious work that 1.3_{-0.9}^{+0.9} % and 2.0_{-1.1}^{+1.1} % of luminousquasars detected in the Sloan Digital Sky Survey exist in the > 4 sigmaoverdense regions within 1.8 and 3.0 arcmin separations, respectively.Therefore, we suggest that the galaxy number densities around quasars areindependent of their luminosity, and most quasars do not preferentially appearin the richest protocluster regions at z ~ 4. The lack of an apparent positivecorrelation between the quasars and the protoclusters implies that: i) thegas-rich major merger rate is relatively low in the protocluster regions, ii)most high-z quasars may appear through secular processes, or iii) somedust-obscured quasars exist in the protocluster regions.

Faint Quasars Live in the Same Number Density Environments as Lyman Break Galaxies at z ~ 4