This is an announcement for the paper "Probabilistic estimates for tensor products of random vectors" by David Alonso-Gutierrez, Markus Passenbrunner and Joscha Prochno. Abstract: We prove some probabilistic estimates for tensor products of random vectors. As an application we obtain embeddings of certain matrix spaces into $L_1$. Archive classification: math.FA Mathematics Subject Classification: 46B09, 46B07, 46B28, 46B45 Remarks: 14 pages Submitted from: joscha.prochno@jku.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.5423 or http://arXiv.org/abs/1404.5423