摘要：We study the singularity probability of random integer matrices. Concretely, the probability that a random n × n matrix, with integer entries chosen uniformly from {-m,…,m}, is singular. This problem has been well studied in two regimes: large n and constant m; or large m and constant n. In this paper, we extend previous techniques to handle the regime where both n,m are large. We show that the probability that such a matrix is singular is m^{-cn} for some absolute constant c > 0. We also provide some connections of our result to coding theory.
