BEACON: JWST NIRCam Pure-parallel Imaging Survey. III. Constraints on the UV LF and the Clustering of z~7-14 Galaxies

The James Webb Space Telescope (JWST) has extended the frontier of galaxy detection to redshifts z>11, finding a high abundance of UV-bright sources that challenge theoretical models. However, most current results come from just a few fields, introducing uncertainties due to cosmic variance. Here, we constrain z~7-14 UV luminosity functions (LFs) over ~400 arcmin^2 across 36 independent sightlines from DR2 of BEACON, a JWST pure-parallel NIRCam multi-band imaging survey. We identify 164 7<z<12 galaxy candidates: 150 F090W-, 14 F115W-, and no robust F150W-dropouts. Based on 11 pointings overlapping with public JWST spectroscopy, we observe 100% purity. Our z~7.5 UV LF agrees with previous bright-end measurements but yields lower number densities at $-21\leq M_\mathrm{UV}\leq-19$. At z~10, our measurements are lower than most photometric JWST results but match spectroscopic constraints, consistent with the high purity of our selection. The LFs at z~7.5 and z~10 are consistent with pre-JWST models, while our limits at z>13 do not rule out a possible excess. We measure significant clustering of bright ($M_\mathrm{UV}<-20.5$) galaxies at 7<z<10. Fields hosting such sources are approximately three times more likely to be overdense relative to the full survey, implying that UV-bright galaxies preferentially reside in the most massive halos at these redshifts. Comparing with semi-numerical simulations, we estimate that $M_{\mathrm{UV}} < -20.5$ galaxies inhabit halos ~0.9 dex less massive at z~11 than at z~7, consistent with a shift to higher star formation rates. However, their observed clustering exceeds predictions from pre-JWST luminosity-halo mass relations, suggesting these sources reside in more massive halos than previously modelled and/or multiple halo occupation.