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abstract: |
    We use the UKIDSS Ultra-deep survey (UDS), currently the deepest panoramic near infra-red survey, together with deep Subaru optical imaging to measure the clustering, number counts and luminosity function of galaxies at $z\sim 2$ selected using the BzK selection technique. We find that both star-forming (sBzK) and passive (pBzK) galaxies, to a magnitude limit of $K_{AB} <
    23$, are strongly clustered. The passive galaxies are the most strongly clustered population, with scale lengths of $r_0 =
    15.0^{+1.9}_{-2.2}$h$^{-1}$Mpc compared with $r_0 =
    6.75^{+0.34}_{-0.37}$h$^{-1}$Mpc for star-forming galaxies. The direct implication is that passive galaxies inhabit the most massive dark-matter halos, and are thus identified as the progenitors of the most massive galaxies at the present day. In addition, the pBzKs exhibit a sharp flattening and potential turn-over in their number counts, in agreement with other recent studies. This plateau cannot be explained by the effects of incompleteness. We conclude that only very massive galaxies are undergoing passive evolution at this early epoch, consistent with the downsizing scenario for galaxy evolution. Assuming a purely passive evolution for the pBzKs from their median redshift to the present day, their luminosity function suggests that only $\sim 2.5 \%$ of present day massive 