Complex networks are key to describing the connected nature of the society that we live in.
This book, the second of two volumes, describes the local structure of random graph models …

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 …

The theory of random measures is a key area of modern probability theory, arguably as rich
and important as martingale theory, ergodic theory, or probabilistic potential theory, to …

The natural habitat of most Bayesian methods is data represented by exchangeable
sequences of observations, for which de Finetti's theorem provides the theoretical …

We establish the satisfiability threshold for random k-SAT for all k≥ k0. That is, there exists a
limiting density αs (k) such that a random k-SAT formula of clause density α is with high …

We introduce and develop a theory of limits for sequences of sparse graphs based on $ L^ p
$ graphons, which generalizes both the existing $ L^\infty $ theory of dense graph limits and …

These lecture notes are intended to be used for master courses, where the students have a
limited prior knowledge of special topics in probability. Therefore, we have included many of …

These expository notes are centered around the circular law theorem, which states that the
empirical spectral distribution of an× n random matrix with iid entries of variance 1/n tends to …

We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral
invariants of sequences of locally symmetric spaces. Our main results are uniform versions …

We give new formulas for the asymptotics of the number of spanning trees of a large graph.
A special case answers a question of McKay [Europ. J. Combin. 4 149–160] for regular …