Upper bound for intermediate singular values of random matrices

In this paper, we prove that an n×nn×n matrix A with independent centered subgaussian entries satisfiessn+1−l(A)≤C1tln with probability at least 1−exp⁡(−C2tl)1−exp⁡(−C2tl). This yields sn+1−l(A)∼cln in combination with a known lower bound. These results can be generalized to the rectangular matrix case.