  We establish new tail estimates for order statistics and for the Euclidean
norms of projections of an isotropic log-concave random vector. More generally,
we prove tail estimates for the norms of projections of sums of independent
log-concave random vectors, and uniform versions of these in the form of tail
estimates for operator norms of matrices and their sub-matrices in the setting
of a log-concave ensemble. This is used to study a quantity $A_{k,m}$ that
controls uniformly the operator norm of the sub-matrices with $k$ rows and $m$
columns of a matrix $A$ with independent isotropic log-concave random rows. We
apply our tail estimates of $A_{k,m}$ to the study of Restricted Isometry
Property that plays a major role in the Compressive Sensing theory.
