Under rather general conditions
on the matrix entries, we obtain estimates for the probability distribution of
the norm of a random matrix transformation from ln2 to lmq(2 ≦ q < ∞).
Asymptotically, the expected norm is remarkably small and this enables us to
produce an interesting class of bounded linear operators from l2 to lq. As an
application, we complete the characterization of (p,q)-absolutely summing operators
on Hilbert space, thereby answering a question left open by several previous
authors.
