Lucas Benigni

collaborators

4 papers

math.PR2026

Hadamard product of independent random sample covariance matrices with correlation structure

Lucas Benigni, Ziyad Zaklani

We compute the asymptotic empirical eigenvalue distribution of the matrix $M = ⨀_{i = 1}^{k} \frac{1}{d _{i}} X^{(i)} X^{(i)}^{⊤}$ where $X^{(i)} \in R^{n \times d_{i}}$ are i…

math.PR2025

Convergence of local eigenvector processes of generalized Wigner matrices

Lucas Benigni, Mohammadreza Rezaei Feyzabady

We prove convergence of eigenvector processes of the form $(N ⟨ u_{k}, A_{t} u_{k} ⟩)_{t \in [0, 1]}$ where $u_{k}$ is a bulk eigenvector of generali…

math.PR2025

Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling

Lucas Benigni, Elliot Paquette

We compute the asymptotic eigenvalue distribution of the neural tangent kernel of a two-layer neural network under a specific scaling of dimension. Namely, if $X\in\mathbb{R}^{n\ti…

math.PR2025

Eigenvalue distribution of the Hadamard product of sample covariance matrices in a quadratic regime

Sebastien Abou Assaly, Lucas Benigni

In this note, we prove that if $X \in R^{n \times d}$ and $Y \in R^{n \times p}$ are two independent matrices with i.i.d entries then the empirical spectral distributio…