Related papers: The cone percolation on $\bbT_d$
In this paper we study the interplay between epidemic spreading and risk perception on multiplex networks. The basic idea is that the effective infection probability is affected by the perception of the risk of being infected, which we…
We introduce a stochastic model which describes diffusions of tweets on the Twitter network. By dividing the followers into generations, we describe the dynamics of the tweet diffusion as a random multiplicative process. We confirm our…
In earlier rumor spreading models, at each time step nodes contact all of their neighbors. In more realistic scenario it is possible that a node may contact only some of its neighbors to spread the rumor. Therefore it is must in real world…
One major function of social networks (e.g., massive online social networks) is the dissemination of information, such as scientific knowledge, news, and rumors. Information can be propagated by the users of the network via natural…
We introduce here a multi-type bootstrap percolation model, which we call T-Bootstrap Percolation (T-BP), and apply it to study information propagation in social networks. In this model, a social network is represented by a graph G whose…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
We introduce the simplest model which relates the emergence of collective social/economic phenomena to the existence of a (possibly self-organized) percolation transition. We suggest a series of extensions to financial, economic, political…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
In this work we study a branching particle system of diffusion processes on the real line interacting through their rank in the system. Namely, each particle follows an independent Brownian motion, but only K $\ge$ 1 particles on the far…
Studying information propagation dynamics in social media can elucidate user behaviors and patterns. However, previous research often focuses on single platforms and fails to differentiate between the nuanced roles of source users and other…
Models of meme propagation on social networks, in which memes compete for limited user attention, can successfully reproduce the heavy-tailed popularity distributions observed in online settings. While system-wide popularity distributions…
We study the diffusion of influence in random multiplex networks where links can be of $r$ different types, and for a given content (e.g., rumor, product, political view), each link type is associated with a content dependent parameter…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
This article studies the dynamics of a finite chain with infinite components. The equation which permits us to find the probability distribution of the chain length is constructed and analysed. This research is a continuation of paper…
Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic "puzzle graph" by using connectivity properties of a random "people graph" on the same set of vertices. We presume the Erdos--Renyi…
Condensation phenomenon is often observed in social networks such as Twitter where one "superstar" vertex gains a positive fraction of the edges, while the remaining empirical degree distribution still exhibits a power law tail. We…
Traditional percolation theory assumes static microscopic rules, limiting its ability to describe real-world complex systems where macroscopic order actively regulates local interactions. Here, we introduce feedback percolation, an unified…
In a complex system, perturbations propagate by following paths on the network of interactions among the system's units. In contrast to what happens with the spreading of epidemics, observations of general perturbations are often very…
Interdependent networks are ubiquitous in our society, ranging from infrastructure to economics, and the study of their cascading behaviors using percolation theory has attracted much attention in the recent years. To analyze the…