This is an announcement for the paper "Dichotomy theorems for random matrices and closed ideals of operators on $\big(\bigoplus _{n=1}^\infty\ell_1^n \big)_{\mathrm{c}_0}$" by Niels Jakob Laustsen, Edward Odell, Thomas Schlumprecht, and Andras Zsak. Abstract: We prove two dichotomy theorems about sequences of operators into $L_1$ given by random matrices. In the second theorem we assume that the entries of each random matrix form a sequence of independent, symmetric random variables. Then the corresponding sequence of operators either uniformly factor the identity operators on $\ell_1^k$ $(k\in\mathbb N$) or uniformly approximately factor through $\mathrm{c}_0$. The first theorem has a slightly weaker conclusion still related to factorization properties but makes no assumption on the random matrices. Indeed, it applies to operators defined on an arbitrary sequence of Banach spaces. These results provide information on the closed ideal structure of the Banach algebra of all operators on the space $\big(\bigoplus_{n=1}^\infty\ell_1^n \big)_{\mathrm{c}_0}$. Archive classification: math.FA Mathematics Subject Classification: 47L10 (primary), 46B09, 46B42, 47L20, 46B45 (secondary) Remarks: 22 pages Submitted from: andras.zsak@maths.nottingham.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.2923 or http://arXiv.org/abs/1009.2923