Approximate Spielman-Teng theorems for the least singular value of random combinatorial matrices

An approximate Spielman-Teng theorem for the least singular value sn(Mn) of a random n × square matrix Mn is statement following form: there exist constants C, c > 0 such that all ? 0, Pr(sn(Mn) ? ?) ? nC? + exp(?nc). The goal this paper to develop simple and novel framework proving results discrete matrices. As an application, we prove {0, 1}-valued matrices, each whose rows independent vector with exactly n/2 zero components. This improves on previous work Nguyen Vu, first result in ‘truly combinatorial’ setting.