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The singularity probability of dense random regular graphs
Abstract
Let Gn,d be a uniformly random simple d-regular graph on n vertices, and let An be its adjacency matrix. For every fixed λ∈(0,1/2), we prove that for any λ(n−1)≤ d≤(1−λ)(n−1), ℙ(An is singular)≤ e−cn, where c>0 depends only on λ, and n is sufficiently large with nd even.
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BibTeX
@misc{song2026singularity,
title = {{The singularity probability of dense random regular graphs}},
author = {Zeyan Song and Hanchao Wang and Shengyan Yin and Kexin Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09380},
eprint = {2610.09380},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09380},
}
RIS
TY - UNPB
TI - The singularity probability of dense random regular graphs
AU - Zeyan Song
AU - Hanchao Wang
AU - Shengyan Yin
AU - Kexin Yu
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09380
UR - https://arxiv.org/abs/2610.09380
AB - Let G_n,d be a uniformly random simple d-regular graph on n vertices, and let A_n be its adjacency matrix. For every fixed λ∈(0,1/2), we prove that for any λ(n−1)≤ d≤(1−λ)(n−1), ℙ(A_n is singular)≤ e^−cn, where c>0 depends only on λ, and n is sufficiently large with nd even.
ER -