On random $\pm 1$ matrices: Singularity and Determinant
Abstract
Description
This papers contains two results concerning random $n \times n$ Bernoulli matrices. First, we show that with probability tending to one the determinant has absolute value $\sqrt {n!} \exp(O(\sqrt(n log n)))$. Next, we prove a new upper bound $.939^n$ on the probability that the matrix is singular. We also give some generalizations to other random matrix models.
25 pages, no figures. Slight numerical corrections to Lemma 2.2
25 pages, no figures. Slight numerical corrections to Lemma 2.2