Largest eigenvalue of positive mean Gaussian matrices

Arijit Chakrabarty; Rajat Subhra Hazra; Moumanti Podder

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arXiv · 2409.05858

Largest eigenvalue of positive mean Gaussian matrices

Arijit Chakrabarty·Rajat Subhra Hazra·Moumanti Podder

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Abstract

This short note studies the fluctuations of the largest eigenvalue of symmetric random matrices with correlated Gaussian entries having positive mean. Under the assumption that the covariance kernel is absolutely summable, it is proved that the largest eigenvalue, after centering, converges in distribution to normal with an explicitly defined mean and variance. This result generalizes known findings for Wigner matrices with independent entries.

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Arijit Chakrabarty, Rajat Subhra Hazra, Moumanti Podder. 2024-09-09. Largest eigenvalue of positive mean Gaussian matrices. https://arxiv.org/abs/2409.05858

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