We investigate random graphs on the points of a Poisson process in d-dimensional space,
which combine scale-free degree distributions and long-range effects. Every Poisson point …

We investigate a class of growing graphs embedded into the d-dimensional torus where
new vertices arrive according to a Poisson process in time, are randomly placed in space …

We study geometric random graphs defined on the points of a Poisson process in d-
dimensional space, which additionally carry independent random marks. Edges are …

Scale-free percolation is a stochastic model for complex networks. In this spatial random
graph model, vertices are linked by an edge with probability depending on independent and …

Abstract Let X 1, X 2,… be iid random variables with values in Z d satisfying PX 1= x= PX
1=− x= Θ‖ x‖− s for some s> d. We show that the random walk defined by S n=∑ k= 1 n X …

The traditional spatial planning model has a large error and poor spatial planning effect,
which cannot adapt to the construction of classical gardens. The flow spatial planning model …

We study three preferential attachment models where the parameters are such that the
asymptotic degree distribution has infinite variance. Every edge is equipped with a …

We study the evolution of the graph distance and weighted distance between two fixed
vertices in dynamically growing random graph models. More precisely, we consider …

The purpose of this note is to demonstrate an analogy of the concepts of weak local limits in
the theory of random graphs and of tangent measures in geometric measure theory. We …

In this thesis, we study long-range percolation at critical phases. We consider the graph
distances for the long-range percolation graph with critical decay parameter and we provide …