Let be a random matrix with i.i.d. entries. We show that for fixed ,
We thank Jordan Ellenberg for a Twitter question which motivated the present work. We also thank Han Huang for sharing a preliminary version of  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.
"Rank deficiency of random matrices." Electron. Commun. Probab. 27 1 - 9, 2022. https://doi.org/10.1214/22-ECP455