These notes attempt to provide an elementary introduction to the one-dimensional discrete-
time branching random walk and to exploit its spinal structure. They begin with the case of …

The present book offers a detailed treatment of perturbed random walks, perpetuities, and
random processes with immigration. These objects are of major importance in modern …

We study the elephant random walk in arbitrary dimension $ d\geq 1$. Our main focus is the
limiting random variable appearing in the superdiffusive regime. Building on a link between …

This paper studies the distribution of a family of rankings, which includes Google's
PageRank, on a directed configuration model. In particular, it is shown that the distribution of …

The focus of this work is the asymptotic analysis of the tail distribution of Google's PageRank
algorithm on large scale-free directed networks. In particular, the main theorem provides the …

Let Z be a random variable with values in a proper closed convex cone, A a random
endomorphism of C and N a random integer. We assume that Z, A, N are independent …

Given a sequence (C, T)=(C, T 1, T 2,...) of real-valued random variables with T j≥ 0 for all
j≥ 1 and almost surely finite N= sup j≥ 1: T j> 0, the smoothing transform associated with …

We propose and analyze a mathematical model for the evolution of opinions on directed
complex networks. Our model generalizes the popular DeGroot and Friedkin-Johnsen …

We extend Goldie's (1991) implicit renewal theorem to enable the analysis of recursions on
weighted branching trees. We illustrate the developed method by deriving the power-tail …

Consider distributional fixed point equations of the form where f (⋅) is a possibly random
real-valued function, N∈{0, 1, 2, 3,…}∪{∞},[Formula: see text] are real-valued random …