Tight Asymptotic of Probability of singularity of n x n Random Matrix with Uniform Distributed \pm 1 Entries

TL;DR

This paper proves the conjecture regarding the probability of singularity for n x n Bernoulli ±1 matrices and provides an asymptotic expansion of this probability.

Contribution

It offers a rigorous proof of the conjecture and derives the asymptotic behavior of the singularity probability for such matrices.

Findings

Confirmed the conjecture on singularity probability

Derived the asymptotic expansion of Pn

Enhanced understanding of random Bernoulli matrices

Abstract

We prove the conjecture about the probability that Pn of Bernulli +- 1 square matrix to be singular and asymptotic expansion of Pn.