Romain Allez

collaborators

3 papers

math.PR2025

The Eigenvector Bead Process

Antonin Barbe, Benjamin De Bruyne, Romain Allez

We investigate the overlap matrix between the eigenvectors of a Wigner matrix $H_{N + K}$ of size $(N + K) \times (N + K)$ and those of its principal minor $H_{N}$ of size $N \times N$ , for b…

math.PR2025

Eigenvector Overlaps of Random Covariance Matrices and their Submatrices

Elie Attal, Romain Allez

We consider the singular vectors of any $m \times n$ submatrix of a rectangular $M \times N$ Gaussian matrix and study their asymptotic overlaps with those of the full matrix, in t…

math.PR2024

Interlacing Eigenvectors of Large Gaussian Matrices

Elie Attal, Romain Allez

We consider the eigenvectors of the principal minor of dimension $n < N$ of the Dyson Brownian motion in $R^{N}$ and investigate their asymptotic overlaps with the eigenvec…