## The smallest singular value of very sparse random matrices with non-zero diagonal

#### Konstantin TikhomirovPrinceton University

Let A be an n by n random matrix with independent identically distributed entries, such that probability that an entry is non-zero is sublogarithmic in n. In particular, this implies that with large probability some of rows and columns of A are zero. In this talk, I will consider the problem of estimating the smallest singular value of shifted matrix A-zI, for a non-zero complex number z. This estimate is crucial in studying the limiting spectral distribution for a sequence of very sparse random matrices.
Based on a joint work with Mark Rudelson.

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