Related papers: Competing first passage percolation on random regu…
Spreading of either information or matter can often be treated as a network problem. It can be of great importance to be able to estimate the likelihood that spreading through a network reaches essentially the entire network while still not…
The emergence and wide-spread use of online social networks has led to a dramatic increase on the availability of social activity data. Importantly, this data can be exploited to investigate, at a microscopic level, some of the problems…
Competition is one of the most fundamental phenomena in physics, biology and economics. Recent studies of the competition between innovations have highlighted the influence of switching costs and interaction networks, but the problem is…
Many processes of spreading and diffusion take place on temporal networks, and their outcomes are influenced by correlations in the times of contact. These correlations have a particularly strong influence on processes where the spreading…
Understanding what types of phenomena lead to discontinuous phase transitions in the connectivity of random networks is an outstanding challenge. Here we show that a simple stochastic model of graph evolution leads to a discontinuous…
Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…
In majority bootstrap percolation on a graph G, an infection spreads according to the following deterministic rule: if at least half of the neighbours of a vertex v are already infected, then v is also infected, and infected vertices remain…
Many biological, social, and communication systems can be modeled by ``searchers'' moving through a complex network. For example, intracellular cargo is transported on tubular networks, news and rumors spread through online social networks,…
Dynamical processes taking place on networks have received much attention in recent years, especially on various models of random graphs (including small world and scale free networks). They model a variety of phenomena, including the…
We study a synchronous dispersion process in which $M$ particles are initially placed at a distinguished origin vertex of a graph $G$. At each time step, at each vertex $v$ occupied by more than one particle at the beginning of this step,…
We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of A's takes precedence over that of B's. The model was originally proposed and analyzed in Maragakis et…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
We consider a stochastic aggregation model on Z^d. Start with particles located at the vertices of the lattice, initially distributed according to the product Bernoulli measure with parameter \mu. In addition, there is an aggregate, which…
Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often…
We investigate systems of nature where the common physical processes diffusion and fragmentation compete. We derive a rate equation for the size distribution of fragments. The equation leads to a third order differential equation which we…
The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous…
We prove results for first-passage percolation on the configuration model with i.i.d. degrees having finite mean, infinite variance and i.i.d. weights with strictly positive support of the form Y=a+X, where a is a positive constant. We…
In this paper we consider a simple model of random graph process with {\it hard} copying as follows: At each time step $t$, with probability $0<\alpha\leq 1$ a new vertex $v_t$ is added and $m$ edges incident with $v_t$ are added in the…
In this paper we address the problem of the calculation of the mean first passage time (MFPT) on generic graphs. We focus in particular on the mean first passage time on a node 's' for a random walker starting from a generic, unknown, node…