Related papers: Continuum Cascade Model: Branching Random Walk for…

Cascade models based on dynamical complex networks are proposed as models of turbulent energy cascade. Taking a simple shell model as the initial regular lattice with only nearest neighbor interactions, small world network models are…

We introduce a system of one-dimensional coalescing nonsimple random walks with long range jumps allowing crossing paths and exibiting dependence before coalescence. We show that under diffusive scaling this system converges in distribution…

Cascade models are central to understanding, predicting, and controlling epidemic spreading and information propagation. Related optimization, including influence maximization, model parameter inference, or the development of vaccination…

We consider the complex branching random walk on a dyadic tree with Gaussian weights on the boundary between the diffuse phase and the glassy phase. We study the branching random walk in the space of continuous functions and establish…

Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…

In a critically self--organized model of punctuated equilibrium, boundaries determine peculiar scaling of the size distribution of evolutionary avalanches. This is derived by an inhomogeneous generalization of standard branching processes,…

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…

An avalanche or cascade occurs when one event causes one or more subsequent events, which in turn may cause further events in a chain reaction. Avalanching dynamics are studied in many disciplines, with a recent focus on average avalanche…

Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…

We discuss a model accounting for the creation and development of transport networks based on the Cameo principle which refers to the idea of distribution of resources, including land, water, minerals, fuel and wealth. We also give an…

The deluge of digital information in our daily life -- from user-generated content, such as microblogs and scientific papers, to online business, such as viral marketing and advertising -- offers unprecedented opportunities to explore and…

We study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to…

We propose a random walks based model to generate complex networks. Many authors studied and developed different methods and tools to analyze complex networks by random walk processes. Just to cite a few, random walks have been adopted to…

Many works have been proposed in the literature to capture the dynamics of diffusion in networks. While some of them define graphical markovian models to extract temporal relationships between node infections in networks, others consider…

Random walks on networks are widely used to model stochastic processes such as search strategies, transportation problems or disease propagation. A prominent example of such process is the guiding of naive T cells by the lymph node conduits…

We consider a general discrete-time branching random walk on a countable set X. We relate local, strong local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that,…

Random walks are a common model for exploration and discovery of complex networks. While numerous algorithms have been proposed to map out an unknown network, a complementary question arises: in a known network, which nodes and edges are…

We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…

On a locally finite point set, a navigation defines a path through the point set from one point to another. The set of paths leading to a given point defines a tree known as the navigation tree. In this article, we analyze the properties of…

Coalescing simple random walks in the plane form an infinite tree. A natural directed distance on this tree is given by the number of jumps between branches when one is only allowed to move in one direction. The Brownian web distance is the…