Une br\`eve histoire des perturbations non-hermitiennes de rang un

TL;DR

This paper reviews the history and recent developments in the study of low-rank non-Hermitian perturbations of random matrices, highlighting their applications in physics and neural networks.

Contribution

It provides an overview of non-Hermitian low-rank perturbation models and discusses their significance in various scientific fields.

Findings

Survey of non-Hermitian perturbation models

Discussion of applications in physics and neural networks

Historical overview of research developments

Abstract

Les perturbations de faible rang de matrices al\'eatoires ont \'et\'e au c{\oe}ur de nombreux travaux ces vingt derni\`eres ann\'ees. En particulier, les cas non-hermitiens, moins repr\'esent\'es dans la litt\'erature en r\`egle g\'en\'erale, font ici l'objet d'une attention sp\'eciale en raison de leurs applications \`a la physique et \`a l'\'etude des r\'eseaux de neurones. Petit tour d'horizon. -- A brief history of non-Hermitian perturbations of rank one: Low-rank perturbations of random matrices have been the focus of active research over the past twenty years. We give an overview of different non-Hermitian models, which are generally less represented in the literature, as well as some of their applications in physics and the study of neural networks.