This is an announcement for the paper "The norm of sums of independent non-commutative random variables in $L_p(\ell_1)$" by Marius Junge and Javier Parcet. Abstract: We investigate the norm of sums of independent vector-valued random variables in non-commutative Lp spaces. This allows us to obtain a uniform family of complete embeddings of the Schatten class Sq^n in Sp(lq^m) with optimal order m=n^2. Using these embeddings we show the surprising fact that the sharp type (cotype) index in the sense of operator spaces for Lp[0,1] is min(p,p') (max(p,p')). Similar techniques are used to show that the operator space notions of B-convexity and K-convexity are equivalent. Archive classification: Functional Analysis; Operator Algebras Mathematics Subject Classification: 46L07; 46L52; 46L53 Remarks: 30 pages The source file(s), Lp1.tex: 107978 bytes, is(are) stored in gzipped form as 0403103.gz with size 29kb. The corresponding postcript file has gzipped size 133kb. Submitted from: javier.parcet@uam.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0403103 or http://arXiv.org/abs/math.FA/0403103 or by email in unzipped form by transmitting an empty message with subject line uget 0403103 or in gzipped form by using subject line get 0403103 to: math@arXiv.org.