Probability and Interpolation

An m x n matrix E with n ones and (m — l)/i zeros, which satisfies the Polya condition, may be regular and singular for Birkhoff interpolation. We prove that for random distributed ones, E is singular with probability that converges to one if m, n -» oo. Previously, this was known only if m > (1 + 8)n/log n. For constant m and n -» oo, the probability is asymptotically at least i.