Some estimates of norms of random matrices

Source abstract

We show that for any random matrix ( X i j ) (X_{ij}) with independent mean zero entries $$E ‖ ( X i j ) ‖ ≤ C ( max i ∑ j E X i j 2 + max j ∑ i E X i j 2 + ∑ i j E X i j 4 4 ) , \mathbf {E}\|(X_{ij})\|\leq C \Big (\max _{i}\sqrt {\sum _{j}\mathbf {E} X_{ij}^{2}}+ \max _{j}\sqrt {\sum _{i}\mathbf {E} X_{ij}^{2}}+ \sqrt [4]{\sum _{ij} \mathbf {E} X_{ij}^{4}} \Big ),$$ where C C is some universal constant.