The CNRS recently published a short popularization article on random matrix theory and its applications, ranging from quantum physics to neuroscience and theoretical ecology, based on conversations with Guillaume Dubach and me.
Among other things, it discusses how random matrices and tensors can be used to study general properties of complex systems. In particular, it explains how random matrices can be used to model the stability of a complex ecosystem near an equilibrium point, as well as the resilience of stable equilibria to perturbations, through the lens of recent work by Lilou Thomas, Anis Farès, and Guillaume Dubach.
The article also discusses the natural generalization from random matrices to random tensors, and I contributed a few remarks on why tensors are both considerably harder to understand and particularly relevant to many-body and multipartite problems, notably in quantum information and quantum computing.
The article is in French and can be read here: Les matrices aléatoires : des maths au service de la physique quantique et de l’étude des écosystèmes.
