Recently, it became apparent that a large number of the most interesting structures and
phenomena of the world can be described by networks. To develop a mathematical theory of …

抄録< jats: p> Property (T) is a rigidity property for topological groups, first formulated by D.
Kazhdan in the mid 1960's with the aim of demonstrating that a large class of lattices are …

Ergodic theory in its broadest sense is the study of group actions on measure spaces.
Historically the discipline has tended to concentrate on the framework of integer actions, in …

Presents Results from a Very Active Area of ResearchExploring an active area of
mathematics that studies the complexity of equivalence relations and classification …

We investigate unimodular random networks. Our motivations include their characterization
via reversibility of an associated random walk and their similarities to unimodular quasi …

" The subject of this book is the study of ergodic, measure preserving actions of countable
discrete groups on standard probability spaces. It explores a direction that emphasizes a …

This is an introductory survey of the emerging theory of two new classes of (discrete,
countable) groups, called hyperlinear and sofic groups. They can be characterized as …

This article combines the features of a survey and a research paper. It presents a review of
some results obtained during the last decade in problems related to the dynamics of branch …

The colored neighborhood metric for sparse graphs was introduced by Bollobás and
Riordan [BR11]. The corresponding convergence notion refines a convergence notion …

We give a positive answer, in the measurable-group-theory context, to von Neumann's
problem of knowing whether a non-amenable countable discrete group contains a non …