A general method for obtaining moment inequalities for functions of independent random variables is presented. It is a generalization of the entropy method which has been used to derive concentration inequalities for such functions [Boucheron, Lugosi and Massart Ann. Probab. 31 (2003) 1583–1614], and is based on a generalized tensorization inequality due to Latała and Oleszkiewicz [Lecture Note...

We present deviation inequalities of random operators of the form 1 N ∑N i=1 Xi ⊗ Xi from the average operator E(X ⊗ X), where Xi are independent random vectors distributed as X, which is a random vector in R or in `2. We use these inequalities to estimate the singular values of random matrices with independent rows (without assuming that the entries are independent).