We performed a deep wide-field (6.76 deg^2) near-infrared survey with the VISTA telescope that covers the entire extent of the Carina nebula complex (CNC). The point-source catalog created from these data contains around four million individual objects down to masses of 0.1 M_sun. We present a statistical study of the large-scale spatial distribution and an investigation of the clustering properties of infrared-excesses objects, which are used to trace disk-bearing young stellar objects (YSOs). We find that a (J - H) versus (Ks - [4.5]) color-color diagram is well suited to tracing the population of YSO-candidates (cYSOs) by their infrared excess. We identify 8781 sources with strong infrared excess, which we consider as cYSOs. This sample is used to investigate the spatial distribution of the cYSOs with a nearest-neighbor analysis. The surface density distribution of cYSOs agrees well with the shape of the clouds as seen in our Herschel far-infrared survey. The strong decline in the surface density of excess sources outside the area of the clouds supports the hypothesis that our excess-selected sample consists predominantly of cYSOs with a low level of background contamination. This analysis allows us to identify 14 groups of cYSOs outside the central area. Our results suggest that the total population of cYSOs in the CNC comprises about 164000 objects, with a substantial fraction (~35%) located in the northern, still not well studied parts. Our cluster analysis suggests that roughly half of the cYSOs constitute a non-clustered, dispersed population.
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