  We measure the angular two-point correlation function of sub-millimeter
galaxies (SMGs) from 1.1-millimeter imaging of the COSMOS field with the AzTEC
camera and ASTE 10-meter telescope. These data yields one of the largest
contiguous samples of SMGs to date, covering an area of 0.72 degrees^2 down to
a 1.26 mJy/beam (1-sigma) limit, including 189 (328) sources with S/N greater
than 3.5 (3). We can only set upper limits to the correlation length r_0,
modeling the correlation function as a power-law with pre-assigned slope.
Assuming existing redshift distributions, we derive 68.3% confidence level
upper limits of r_0 < 6-8 h^-1 Mpc at 3.7 mJy, and r_0 < 11-12 h^-1 Mpc at 4.2
mJy. Although consistent with most previous estimates, these upper limits imply
that the real r_0 is likely smaller. This casts doubts on the robustness of
claims that SMGs are characterized by significantly stronger spatial
clustering, (and thus larger mass), than differently selected galaxies at
high-redshift. Using Monte Carlo simulations we show that even strongly
clustered distributions of galaxies can appear unclustered when sampled with
limited sensitivity and coarse angular resolution common to current
sub-millimeter surveys. The simulations, however, also show that unclustered
distributions can appear strongly clustered under these circumstances. From the
simulations, we predict that at our survey depth, a mapped area of two
degrees^2 is needed to reconstruct the correlation function, assuming smaller
beam sizes of future surveys (e.g. the Large Millimeter Telescope's 6" beam
size). At present, robust measures of the clustering strength of bright SMGs
appear to be below the reach of most observations.
