Space of Traffics and Asymptotics of Random Spectra – STARS

Random Matrix Theory developed during the last three decades in numerous fields of mathematics and physics. Free Probability Theory (FPT) is adapted for their analysis in large dimension. Operator-valued free probability and Traffic Probability Theory (TPT) are upgrades of FPT appropriate to describe random matrices which are beyond the usual scope of FPT.

This project aims at fostering new directions of research in the fields of FPT and TPT, via the study of random matrices subject to new symmetries and via new applications. We will investigate questions such as the convergence of the spectrum distributions and the understanding of the outliers, in interaction with the invariances of the random matrix models. Fields of application we shall explore include Random Matrix Theory, Lie group theory, signal detection theory and artificial neural networks.