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2022 Rank deficiency of random matrices
Vishesh Jain, Ashwin Sah, Mehtaab Sawhney
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Electron. Commun. Probab. 27: 1-9 (2022). DOI: 10.1214/22-ECP455

Abstract

Let Mn be a random n×n matrix with i.i.d. Bernoulli(12) entries. We show that for fixed k1,

limn1nlog2P[corankMnk]=k.

Acknowledgments

We thank Jordan Ellenberg for a Twitter question which motivated the present work. We also thank Han Huang for sharing a preliminary version of [6] with us. Finally we are grateful to the anonymous referees for their careful reading of our paper and for numerous comments which have improved the presentation.

Citation

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Vishesh Jain. Ashwin Sah. Mehtaab Sawhney. "Rank deficiency of random matrices." Electron. Commun. Probab. 27 1 - 9, 2022. https://doi.org/10.1214/22-ECP455

Information

Received: 12 March 2021; Accepted: 12 February 2022; Published: 2022
First available in Project Euclid: 23 February 2022

arXiv: 2103.02467
Digital Object Identifier: 10.1214/22-ECP455

Subjects:
Primary: 60B20

Keywords: corank , invertibility , random matrices

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