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Convergence of Kikuchi matrices to Γ-independent and q-Gaussian limits
Abstract
Kikuchi matrices are a family of structured matrices that were introduced to study problems involving tensors and hypergraphs. We show that, as the ambient dimension grows, dense random Kikuchi matrices have a limit described by a system of Γ-independent semicircular elements. This characterizes their limiting spectral distribution and yields improved bounds on their spectral norm, a key quantity in the analysis of algorithms for Tensor PCA. Finally, we show that, in an appropriate double limit, independent Kikuchi matrices converge to the q-Gaussian system, another central object in noncommutative probability.
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BibTeX
@misc{bandeira2026convergence,
title = {{Convergence of Kikuchi matrices to $Γ$-independent and $q$-Gaussian limits}},
author = {Afonso S. Bandeira and Dmitriy Kunisky and Petar Nizić-Nikolac and Lucas Pesenti and Robert Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02008},
eprint = {2610.02008},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02008},
}
RIS
TY - UNPB
TI - Convergence of Kikuchi matrices to Γ-independent and q-Gaussian limits
AU - Afonso S. Bandeira
AU - Dmitriy Kunisky
AU - Petar Nizić-Nikolac
AU - Lucas Pesenti
AU - Robert Wang
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02008
UR - https://arxiv.org/abs/2610.02008
AB - Kikuchi matrices are a family of structured matrices that were introduced to study problems involving tensors and hypergraphs. We show that, as the ambient dimension grows, dense random Kikuchi matrices have a limit described by a system of Γ-independent semicircular elements. This characterizes their limiting spectral distribution and yields improved bounds on their spectral norm, a key quantity in the analysis of algorithms for Tensor PCA. Finally, we show that, in an appropriate double limit, independent Kikuchi matrices converge to the q-Gaussian system, another central object in noncommutative probability.
ER -