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 …

In certain problems in a variety of applied probability settings (from probabilistic analysis of
algorithms to statistical physics), the central requirement is to solve a recursive distributional …

We establish the existence of free energy limits for several sparse random hypergraph
models corresponding to certain combinatorial models on Erdos-Renyi (ER) graph G (N …

We study matchings on sparse random graphs by means of the cavity method. We first show
how the method reproduces several known results about maximum and perfect matchings in …

The independence number of a sparse random graph G (n, m) of average degree d= 2m/n is
well‐known to be with high probability, with in the limit of large d. Moreover, a trivial greedy …

Abstract Recently, Bollobás, Janson and Riordan introduced a family of random graph
models producing inhomogeneous graphs with n vertices and Θ (n) edges whose …

In this article we propose new methods for computing the asymptotic value for the logarithm
of the partition function (free energy) for certain statistical physics models on certain type of …

This paper gives an overview of recent research on the performance evaluation and design
of carousel systems. We discuss picking strategies for problems involving one carousel …

We consider the general problem of finding the minimum weight b-matching on arbitrary
graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has …

In 1981, Karp and Sipser proved a law of large numbers for the matching number of a
sparse Erd\H {o} sR\'enyi random graph, in an influential paper pioneering the so-called …