On the singularity of random matrices with independent entries

2008/01/08 by Laurent Bruneau, François Germinet, Bruneau, Laurent +1
Mathematics · #15A52 #60C05 #Advanced Algebra and Geometry #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0801.1221

openalex publication_date 2008/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider n by n real matrices whose entries are non-degenerate random variables that are independent but non necessarily identically distributed, and show that the probability that such a matrix is singular is O(1/sqrtn). The purpose of this note is to provide a short and elementary proof of this fact using a Bernoulli decomposition of arbitrary non degenerate random variables.

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