Spectral Universality for Matrices with Non-Linear Correlated Entries
Abstract
We establish nonasymptotic spectral comparison results for matrices whose entries are non-linear functions of an iid random field. Under an exponential decay assumption on an 𝕃∞-coupling coefficient, we derive high-probability bounds for the Hausdorff distance between their spectra and those of Gaussian matrices with matching covariance structures. We further derive a comparison with a covariance-matched free model and derive corresponding noncommutative Khintchine-type bounds. The results apply, in particular, to matrices whose entries are nonlinear transformations of causal linear processes, Volterra-type processes, and neural networks. The proof combines finite-memory approximation, block decomposition, Gaussian interpolation, and resolvent estimates.
Related
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BibTeX
@misc{banna2026spectral,
title = {{Spectral Universality for Matrices with Non-Linear Correlated Entries}},
author = {Marwa Banna and Issa-Mbenard Dabo and Florence Merlevède},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39793},
eprint = {2609.39793},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39793},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spectral Universality for Matrices with Non-Linear Correlated Entries
AU - Marwa Banna
AU - Issa-Mbenard Dabo
AU - Florence Merlevède
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39793
UR - https://arxiv.org/abs/2609.39793
AB - We establish nonasymptotic spectral comparison results for matrices whose entries are non-linear functions of an iid random field. Under an exponential decay assumption on an 𝕃^∞-coupling coefficient, we derive high-probability bounds for the Hausdorff distance between their spectra and those of Gaussian matrices with matching covariance structures. We further derive a comparison with a covariance-matched free model and derive corresponding noncommutative Khintchine-type bounds. The results apply, in particular, to matrices whose entries are nonlinear transformations of causal linear processes, Volterra-type processes, and neural networks. The proof combines finite-memory approximation, block decomposition, Gaussian interpolation, and resolvent estimates.
ER -