Rank deficiency of random matrices

2021/03/03 by Jain, Vishesh, Sah, Ashwin, Sawhney, Mehtaab · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2103.02467

Abstract

Let M_n be a random n× n matrix with i.i.d. Bernoulli(1/2) entries. We show that for fixed k≥ 1, lim_{n→ ∞}(1)/(n)log₂ℙ[corank M_n≥ k] = -k.

Cited by

• On random matrices with large corank
• On the rank of a random symmetric matrix in the large deviation regime

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