PreprintCC BY 4.0arXiv
Linear stability and divisibility gaps for Gaussian maxima
Abstract
We study Gaussian maxima arising from isotropic families of unit vectors and show that their excess expected maximum is controlled by the distance from an orthonormal basis. We apply this stability result to correlation matrices with equal nonzero eigenvalues, obtaining an exact minimum when the matrix size is divisible by the rank and a quantitative gap otherwise. In dimension two, we determine the leading asymptotic term and describe the structure of near-optimal configurations. We also obtain covariance-block recovery results and a finite-dimensional lower bound for the higher-rank limiting problem.
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BibTeX
@misc{paatur2026linear,
title = {{Linear stability and divisibility gaps for Gaussian maxima}},
author = {Chahel Paatur},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14086},
eprint = {2610.14086},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14086},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Linear stability and divisibility gaps for Gaussian maxima
AU - Chahel Paatur
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.14086
UR - https://arxiv.org/abs/2610.14086
AB - We study Gaussian maxima arising from isotropic families of unit vectors and show that their excess expected maximum is controlled by the distance from an orthonormal basis. We apply this stability result to correlation matrices with equal nonzero eigenvalues, obtaining an exact minimum when the matrix size is divisible by the rank and a quantitative gap otherwise. In dimension two, we determine the leading asymptotic term and describe the structure of near-optimal configurations. We also obtain covariance-block recovery results and a finite-dimensional lower bound for the higher-rank limiting problem.
ER -