Norms of certain random matrices with dependent entries

We consider certain random matrices with pairwise uncorrelated, but dependent entries, that do not belong to the Marchenko-Pastur ensemble (sample covariance matrices), and obtain bounds on their largest eigenvalue. The results show that the higher order correlations have a strong influence on the norm. While the proofs follow the well-known method of calculating the expectation of the trace of high powers of the matrices, the ensuing combinatorial problems are of a novel type.