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Pré-Publication, Document De Travail Année : 2023

Spectral Phase Transitions in Non-Linear Wigner Spiked Models

Justin Ko
  • Fonction : Auteur
Florent Krzakala
  • Fonction : Auteur
Pierre Mergny
  • Fonction : Auteur
Lenka Zdeborová
  • Fonction : Auteur

Résumé

We study the asymptotic behavior of the spectrum of a random matrix where a non-linearity is applied entry-wise to a Wigner matrix perturbed by a rank-one spike with independent and identically distributed entries. In this setting, we show that when the signal-to-noise ratio scale as $N^{\frac{1}{2} (1-1/k_\star)}$, where $k_\star$ is the first non-zero generalized information coefficient of the function, the non-linear spike model effectively behaves as an equivalent spiked Wigner matrix, where the former spike before the non-linearity is now raised to a power $k_\star$. This allows us to study the phase transition of the leading eigenvalues, generalizing part of the work of Baik, Ben Arous and Pech\'e to these non-linear models.

Dates et versions

hal-04409975 , version 1 (22-01-2024)

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Citer

Alice Guionnet, Justin Ko, Florent Krzakala, Pierre Mergny, Lenka Zdeborová. Spectral Phase Transitions in Non-Linear Wigner Spiked Models. 2024. ⟨hal-04409975⟩
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