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Large corank of dense random regular digraphs
Abstract
Let 1≤ k≤ n and let A be the adjacency matrix of a uniformly random d-regular directed graph on n vertices. Suppose that λn≤ d ≤ (1−λ)n for a fixed 0<λ≤ 1/2. We show that there exists cλ>0 depending only on λ such that ℙ[rank(A)≤ n−k]≤ 2e−cλ kn. This gives a large corank extension of the exponential singularity bound of Jain, Sah, and Sawhney.
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BibTeX
@misc{liang2026large,
title = {{Large corank of dense random regular digraphs}},
author = {Huaijin Liang and Kexin Yu and Tingzhou Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06788},
eprint = {2610.06788},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06788},
}
RIS
TY - UNPB
TI - Large corank of dense random regular digraphs
AU - Huaijin Liang
AU - Kexin Yu
AU - Tingzhou Yu
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06788
UR - https://arxiv.org/abs/2610.06788
AB - Let 1≤ k≤ n and let A be the adjacency matrix of a uniformly random d-regular directed graph on n vertices. Suppose that λn≤ d ≤ (1−λ)n for a fixed 0<λ≤ 1/2. We show that there exists c_λ>0 depending only on λ such that ℙ[rank(A)≤ n−k]≤ 2e^−c_λ kn. This gives a large corank extension of the exponential singularity bound of Jain, Sah, and Sawhney.
ER -