Related papers: Percolation for D2D Networks on Street Systems
Let $X$ be either $Z^d$ or the points of a Poisson process in $R^d$ of intensity 1. Given parameters $r$ and $p$, join each pair of points of $X$ within distance $r$ independently with probability $p$. This is the simplest case of a…
In this paper, we consider a vehicular network in which the wireless nodes are located on a system of roads. We model the roadways, which are predominantly straight and randomly oriented, by a Poisson line process (PLP) and the locations of…
A common way of classifying network connectivity is the association of the nodal degree distribution to specific probability distribution models. During the last decades, researchers classified many networks using the Poisson or Pareto…
We consider a version of continuum long-range percolation on finite boxes of $\mathbb{R}^d$ in which the vertex set is given by the points of a Poisson point process and each pair of two vertices at distance $r$ is connected with…
We introduce and analyze models for the propagation of malware in pure D2D networks given via stationary Cox-Gilbert graphs. Here, the devices form a Poisson point process with random intensity measure $\lambda\Lambda$, where $\Lambda$ is…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
A new random geometric graph model, the so-called secrecy graph, is introduced and studied. The graph represents a wireless network and includes only edges over which secure communication in the presence of eavesdroppers is possible. The…
Motivated by multi-hop communication in unreliable wireless networks, we present a percolation theory for time-varying networks. We develop a renormalization group theory for a prototypical network on a regular grid, where individual links…
It has been shown that deploying device-to-device (D2D) networks in urban environments requires equipping a considerable proportion of crossroads with relays. This represents a necessary economic investment for an operator. In this work, we…
The functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong…
Percolation transition is widely observed in networks ranging from biology to engineering. While much attention has been paid to network topologies, studies rarely focus on critical percolation phenomena driven by network dynamics. Using…
Vehicle-to-infrastructure (V2I) communication may provide high data rates to vehicles via millimeter-wave (mmWave) microcellular networks. This paper uses stochastic geometry to analyze the coverage of urban mmWave microcellular networks.…
We introduce a continuum percolation model defined on the points of a d-dimensional homogeneous Poisson process. Each Poisson point is connected to all points within its connection range, which depends on the distances to the other Poisson…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…
Liquid diodes are surface structures that facilitate the flow of liquids in a specific direction. When these structures are within the capillary regime, they promote liquid transport without the need for external forces. In nature, they are…
We study percolation of two-sided level sets for the discrete Gaussian free field (DGFF) in 2D. For a DGFF $\varphi$ defined in a box $B_N$ with side length $N$, for $C$ large enough, there exist low crossings in the set of vertices $z$…
Much work has been devoted to studying percolation of networks and interdependent networks under varying levels of failures. Researchers have considered many different realistic network structures, but thus far no study has incorporated the…
Device-to-device (D2D) communications over licensed wireless spectrum has been recently proposed as a promising technology to meet the capacity crunch of next generation cellular networks. However, due to the high mobility of cellular…
Static wireless networks are by now quite well understood mathematically through the random geometric graph model. By contrast, there are relatively few rigorous results on the practically important case of mobile networks, in which the…
Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…