In this paper, the coverage performance in Heterogeneous Networks (HetNet) with n-interacted transmission nodes is being analyzed statistically. With HetNets a significant improvement in throughput is expected, but one major drawback in the successful commercial implementation of HetNets is...

Consider the model where particles are initially distributed on Zd,d≥2, according to a Poisson point process of intensity λ0, and are moving in continuous time as independent simple symmetric random walks. We study the escape versus detection problem, in which the target, initially placed at...

Consider a sequence of independent Poisson point processes X1,X2,… with densities λ1,λ2,…, respectively, and connection functions g1,g2,… defined by gn(r)=g(nr), for r0 and for some integrable function g. The Poisson random connection model (Xn,λn,gn) is a random graph with vertex set...

We consider a neutral dynamical model of biological diversity, where individuals live and reproduce independently. They have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant rate b. Such a genealogical tree is usually called a...

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the...

Let m be a random tessellation in Rd, d≥1, observed in a bounded Borel subset W and f(⋅) be a measurable function defined on the set of convex bodies. A point z(C), called the nucleus of C, is associated with each cell C of m. Applying f(⋅) to all the cells of m, we investigate the order...

We establish relations of stochastic comparison among point processes elements of the set of alpha-permanental point processes. This set contains in particular, the determinantal point processes, the Poisson point processes and the permanental point processes. We show that these three classes of...