Đề tài " Invertibility of random matrices: norm of the inverse "

Let A be an n × n matrix, whose entries are independent copies of a centered random variable satisfying the subgaussian tail estimate. We prove that the operator norm of A−1 does not exceed Cn3/2 with probability close to 1. 1. Introduction Let A be an n × n matrix, whose entries are independent, identically distributed random variables. The spectral properties of such matrices, in particular invertibility, have been extensively studied (see, e.g. [M] and the survey [DS]). While A is almost surely invertible whenever its entries are absolutely continuous, the case of discrete entries is highly nontrivial. ...