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 …

In this review we summarise recent results for the complex eigenvalues and singular values
of finite products of finite size random matrices, their correlation functions and asymptotic …

We study various methods to generate ensembles of random density matrices of a fixed size
N, obtained by partial trace of pure states on composite systems. Structured ensembles of …

We show that under suitable assumptions, we have a one-to-one correspondence between
classical groups and free quantum groups, in the compact orthogonal case. We classify the …

We discuss the product of M rectangular random matrices with independent Gaussian
entries, which have several applications, including wireless telecommunication and …

We consider the product of M quadratic random matrices with complex elements and no
further symmetry, where all matrix elements of each factor have a Gaussian distribution. This …

Abstract Akemann, Ipsen and Kieburg recently showed that the squared singular values of
products of M rectangular random matrices with independent complex Gaussian entries are …

Easy quantum groups form a class of compact matrix quantum groups which are completely
determined by set partitions. They have been defined in 2009 by Banica and Speicher in the …

We study easy quantum groups, a combinatorial class of orthogonal quantum groups
introduced by Banica–Speicher in 2009. We show that there is a countable descending …

For random integer matrices M 1,…, M k∈ Mat n (Z) with independent entries, we study the
distribution of the cokernel Cok (M 1⋯ M k) of their product. We show that this distribution …