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 …

Consider a graph G=(V, E) G=(V, E) and an initial random coloring where each vertex v ∈ V
v∈ V is blue with probability P_b P b and red otherwise, independently from all other …

In this paper we explore first passage percolation (FPP) on the Erdős–Rényi random graph
Gn (pn), where we assign independent random weights, having an exponential distribution …

We consider first passage percolation on the configuration model with n vertices, and
general independent and identically distributed edge weights assumed to have a density …

In this book, we discuss stochastic processes on random graphs. The understanding of such
processes is interesting from an applied perspective, since random graphs serve as models …

In standard randomized (push-pull) rumor spreading, nodes communicate in synchronized
rounds. In each round every node contacts a random neighbor in order to exchange the …

The asynchronous push&pull protocol, a randomized distributed algorithm for spreading a
rumour in a graph G, is defined as follows. Independent exponential clocks of rate 1 are …

In this paper we study the impact of random exponential edge weights on the distances in a
random graph and, in particular, on its diameter. Our main result consists of a precise …

In this paper, we study the impact of edge weights on distances in sparse random graphs.
We interpret these weights as delays and take them as independent and identically …

We consider the performance of information propagation through social networks in a
scenario where each user has a budget of attention, that is, a constraint on the frequency …