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 …

Graphs drawn on two-dimensional surfaces have always attracted researchers by their
beauty and by the variety of difficult questions to which they give rise. The theory of such …

The aim of this paper is to introduce a notion of L2-homology in the context of von Neumann
algebras. Finding a suitable (co) homology theory for von Neumann algebras has been a …

Random matrix theory has developed in the last few years, in connection with various fields
of mathematics and physics. These notes emphasize the relation with the problem of …

We prove that a normalized sequence of multiple Wigner integrals (in a fixed order of free
Wigner chaos) converges in law to the standard semicircular distribution if and only if the …

For a compact quantum group $\mathbb {G} $ of Kac type, we study the existence of a Haar
trace-preserving embedding of the von Neumann algebra $ L^\infty (\mathbb {G}) $ into an …

We prove that the von Neumann algebras of quantum permutation groups and quantum
reflection groups have the Connes embedding property. We do this by establishing several …

We investigate the large N limit of spectral measures of matrices which relate to the Gibbs
measures of a number of statistical mechanical systems on random graphs. These include …

In this paper, we prove that in small parameter regions, arbitrary unitary matrix integrals
converge in the large N limit and match their formal expansion. Secondly we give a …

Графы, нарисованные на двумерных поверхностях, всегда привлекали
исследователей своей красотой и разнообразием связанных с ними трудных …