Singularity of Random Matrices over Finite Fields

2010/12/10 by Kenneth Maples, Maples, Kenneth · 3 citations
Mathematics · #15B33 #15B52 (Primary) #60C05 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1012.2372

openalex publication_date 2010/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be an n × n random matrix with iid entries over a finite field of order q. Suppose that the entries do not take values in any additive coset of the field with probability greater than 1 - α for some fixed 0 < α< 1. We show that the singularity probability converges to the uniform limit with an exponentially small error depending only on α. We also show that the distribution of the determinant of A converges to its limiting distribution at an exponential rate.

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