Related papers: Long-Range Navigation on Complex Networks using L\…
Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical…
We introduce a formalism based on a continuous time approximation, to study the characteristics of Page Rank random walks. We find that the diffusion of the occupancy probability has a dynamics that exponentially "forgets" the initial…
In this paper, we present an overview of different types of random walk strategies with local and non-local transitions on undirected connected networks. We present a general approach to analyzing these strategies by defining the dynamics…
We introduce a formalism of fractional diffusion on networks based on a fractional Laplacian matrix that can be constructed directly from the eigenvalues and eigenvectors of the Laplacian matrix. This fractional approach allows random walks…
We study the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. We deduce analytical expressions for the stationary occupation probability and for the mean and global first…
Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not…
Search strategies based on random walk processes with long-tailed jump length distributions (Levy walks) on the one hand and intermittent behavior switching between local search and ballistic relocation phases on the other, have been…
The spectral theory of random walks on networks of arbitrary topology can be readily extended to study random walks and L\'evy flights subject to resetting on these structures. When a discrete-time process is stochastically brought back…
Complex networks have been found to provide a good representation of the structure of knowledge, as understood in terms of discoverable concepts and their relationships. In this context, the discovery process can be modeled as agents…
Random walks have been proposed as a simple method of efficiently searching, or disseminating information throughout, communication and sensor networks. In nature, animals (such as ants) tend to follow correlated random walks, i.e., random…
We study random walks with stochastic resetting to the initial position on arbitrary networks. We obtain the stationary probability distribution as well as the mean and global first passage times, which allow us to characterize the effect…
L\'evy walks are random walk processes whose step-lengths follow a long-tailed power-law distribution. Due to their abundance as movement patterns of biological organisms, significant theoretical efforts have been devoted to identifying the…
In the present work, we study random walks on complex networks subject to stochastic resetting when the resetting probability is node-dependent. Using a renewal approach, we derive the exact expressions of the stationary occupation…
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…
Efficient techniques to navigate networks with local information are fundamental to sample large-scale online social systems and to retrieve resources in peer-to-peer systems. Biased random walks, i.e. walks whose motion is biased on…
The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…
We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…
L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…
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…
A L\'evy random medium, in a given space, is a random point process where the distances between points, a.k.a. targets, are long-tailed. Random walks visiting the targets of a L\'evy random medium have been used to model many (physical,…