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Spectral aspects of random heavy-tailed tensors
Abstract
We introduce heavy-Wigner random tensors and establish the convergence of a generating family of invariant linear forms in their entries together with a central limit theorem. The relevant group actions arise naturally in the study of tensor eigenvalues. Then, we compute the limiting spectral measure of the matrix obtained by contraction of a heavy-Wigner tensor and we derive two applications. The first one concerns the adjacency tensor of a Erdős-Rényi hypergraph. We identify the local weak limit of the hypergraph and study the limiting spectral distribution of the matrix contraction. The second application concerns Lévy tensors whose entries belong to the domain of attraction of an α-stable law.
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BibTeX
@misc{bonnin2026spectral,
title = {{Spectral aspects of random heavy-tailed tensors}},
author = {Remi Bonnin and Alexis Imbert},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.24695},
eprint = {2607.24695},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.24695},
}
RIS
TY - UNPB
TI - Spectral aspects of random heavy-tailed tensors
AU - Remi Bonnin
AU - Alexis Imbert
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2607.24695
UR - https://arxiv.org/abs/2607.24695
AB - We introduce heavy-Wigner random tensors and establish the convergence of a generating family of invariant linear forms in their entries together with a central limit theorem. The relevant group actions arise naturally in the study of tensor eigenvalues. Then, we compute the limiting spectral measure of the matrix obtained by contraction of a heavy-Wigner tensor and we derive two applications. The first one concerns the adjacency tensor of a Erdős-Rényi hypergraph. We identify the local weak limit of the hypergraph and study the limiting spectral distribution of the matrix contraction. The second application concerns Lévy tensors whose entries belong to the domain of attraction of an α-stable law.
ER -