Related papers: Volume explored by a branching random walk on gene…
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time…
Waves propagating through a weakly scattering random medium show a pronounced branching of the flow accompanied by the formation of freak waves, i.e., extremely intense waves. Theory predicts that this strong fluctuation regime is…
We study the impact on shape parameters of an underlying Bienaym\'e-Galton-Watson branching process (height, width and first hitting time), of having a non-spatial branching mechanism with infinite variance. Aiming at providing a…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on…
We consider branching random walks and contact processes on infinite, connected, locally finite graphs whose reproduction and infectivity rates across edges are inversely proportional to vertex degree. We show that when the ambient graph is…
We present the analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from the regular to random behavior with increasing distance from the starting point of the…
We present a graph random walk (GRW) method for the study of charge transport properties of complex molecular materials in the time-of-flight regime. The molecules forming the material are represented by the vertices of a directed weighted…
We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on Barab\'asi-Albert (BA),…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
How to enable efficient analytics over such data has been an increasingly important research problem. Given the sheer size of such social networks, many existing studies resort to sampling techniques that draw random nodes from an online…
We revisit a simple model class for machine learning on graphs, where a random walk on a graph produces a machine-readable record, and this record is processed by a deep neural network to directly make vertex-level or graph-level…
Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…
The territory explored by a random walk is a key property that may be quantified by the number of distinct sites that the random walk visits up to a given time. The extent of this spatial exploration characterizes many important physical,…
Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the…
We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [Tadi\'c, Physica A {\bf 293},…
Branching random flights are key to describing the evolution of many physical and biological systems, ranging from neutron multiplication to gene mutations. When their paths evolve in bounded regions, we establish a relation between the…
In this paper we study the behavior of a continuous time random walk (CTRW) on a stationary and ergodic time varying dynamic graph. We establish conditions under which the CTRW is a stationary and ergodic process. In general, the stationary…
Flow and multicomponent reactive transport in saturated/unsaturated porous media are modeled by ensembles of computational particles moving on regular lattices according to specific random walk rules. The occupation number of the lattice…