PreprintarXiv licencearXiv
Optimal fiber comparisons for random tensors
Abstract
We extend Seginer's matrix norm comparison to tensors with optimal dependence on the tensor order. For a real tensor T of order k≥2 with centered, integrable, independent and identically distributed entries, we prove 𝔼 f(T)≤𝔼lVert TrVertinj ≤ C√(klog k) 𝔼 f(T), where f(T) is the largest Euclidean norm of a one-dimensional fiber and C is universal. The comparison holds for every finite rectangular format, and the entry law may depend on both the dimensions and the tensor order. We show that the factor √(klog k) is optimal by considering Rademacher tensors on [2]k.
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BibTeX
@misc{lin2026optimal,
title = {{Optimal fiber comparisons for random tensors}},
author = {Ziqian Lin and Huangang Lu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39389},
eprint = {2610.39389},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39389},
}
RIS
TY - UNPB
TI - Optimal fiber comparisons for random tensors
AU - Ziqian Lin
AU - Huangang Lu
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39389
UR - https://arxiv.org/abs/2610.39389
AB - We extend Seginer's matrix norm comparison to tensors with optimal dependence on the tensor order. For a real tensor T of order k≥2 with centered, integrable, independent and identically distributed entries, we prove 𝔼 f(T)≤𝔼lVert TrVert_inj ≤ C√(klog k) 𝔼 f(T), where f(T) is the largest Euclidean norm of a one-dimensional fiber and C is universal. The comparison holds for every finite rectangular format, and the entry law may depend on both the dimensions and the tensor order. We show that the factor √(klog k) is optimal by considering Rademacher tensors on [2]^k.
ER -