This book is an invitation to the world of free probability theory. Free probability is a quite
young mathematical theory with many avatars. It owes its existence to the visions of one …

We review methods to calculate eigenvalue distributions of products of large random
matrices. We discuss a generalization of the law of free multiplication to non-Hermitian …

We study random graphs with arbitrary distributions of expected degree and derive
expressions for the spectra of their adjacency and modularity matrices. We give a complete …

This book is aimed at students in communications and signal processing who want to extend
their skills in the energy area. It describes power systems and why these backgrounds are …

Although the spectra of random networks have been studied for a long time, the influence of
network topology on the dense limit of network spectra remains poorly understood. By …

A bstract We give a free probabilistic proposal to compute the fine-grained radiation entropy
for an arbitrary bulk radiation state, in the context of the Penington-Shenker-Stanford-Yang …

We derive a multiplication law for free non-Hermitian random matrices allowing for an easy
reconstruction of the two-dimensional eigenvalue distribution of the product ensemble from …

Abstract Free Probability Theory (FPT) provides rich knowledge for handling mathematical
difficulties caused by random matrices appearing in research related to deep neural …

We investigate the universality of singular value and eigenvalue distributions of matrix-
valued functions of independent random matrices and apply these general results in several …

This is an introductory book on Non-Commutative Probability or Free Probability and Large
Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy …