Singularity probabilities for random matrices over finite fields (Q2726710)

This paper generalizes a result of \textit{L. S. Charlap, H. D. Rees} and \textit{D. P. Robbins} [Discrete Math. 82, No. 2, 153--163 (1990; Zbl 0721.15003)] on when matrices with entries chosen independently from a fixed finite field, of larger and larger size, tend to have the same probability of nonsingularity as with the uniform distribution. The hypothesis that the distribution is not concentrated on a subspace is replaced by a hypothesis that the distribution is not concentrated on a subspace of the form \(aK+b\) where \(K\) is a proper subfield, and the distributions are allowed to vary with \(n\).