Quantifying the Rarity of the Local Super-Volume
  We investigate the extent to which the number of clusters of mass exceeding
$10^{15}\,M_{\odot}\,h^{-1}$ within the local super-volume
($<135\mathrm{\,Mpc}h^{-1}$) is compatible with the standard $\Lambda$CDM
cosmological model. Depending on the mass estimator used, we find that the
observed number $N$ of such massive structures can vary between $0$ and $5$.
Adopting $N=5$ yields $\Lambda$CDM likelihoods as low as $2.4\times 10^{-3}$
(with $\sigma_8=0.81$) or $3.8\times 10^{-5}$ (with $\sigma_8=0.74$). However,
at the other extreme ($N=0$), the likelihood is of order unity. Thus, while
potentially very powerful, this method is currently limited by systematic
uncertainties in cluster mass estimates. This motivates efforts to reduce these
systematics with additional observations and improved modelling.
