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Exponential Rank Bounds for Random Matrices
Abstract
Fix b∈(0,1), let 1≤ k≤ n, and let A=(Aij) be an n× n random matrix with independent real entries satisfying supx∈ℝℙ{Aij=x}≤ b<1 (1≤ i,j≤ n). We show that there exists c>0 such that ℙ{rank A≤ n−k}≤ exp(−cnk), 1≤ k≤ n.
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BibTeX
@misc{polavarapu2026exponential,
title = {{Exponential Rank Bounds for Random Matrices}},
author = {Achintya Raya Polavarapu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.25204},
eprint = {2606.25204},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.25204},
}
RIS
TY - UNPB
TI - Exponential Rank Bounds for Random Matrices
AU - Achintya Raya Polavarapu
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2606.25204
UR - https://arxiv.org/abs/2606.25204
AB - Fix b∈(0,1), let 1≤ k≤ n, and let A=(A_ij) be an n× n random matrix with independent real entries satisfying sup_x∈ℝℙ{A_ij=x}≤ b<1 (1≤ i,j≤ n). We show that there exists c>0 such that ℙ{rank A≤ n−k}≤ exp(−cnk), 1≤ k≤ n.
ER -