Related papers: Random walk and trapping processes on scale-free n…
A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…
Nodes can be ranked according to their relative importance within the network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based…
It is well known that many real world networks have the power-law degree distribution (scale-free property). However there are no rigorous results for continuous-time quantum walks on such realistic graphs. In this paper, we analyze…
Performing random walks in networks is a fundamental primitive that has found numerous applications in communication networks such as token management, load balancing, network topology discovery and construction, search, and peer-to-peer…
We study exploration properties of a random walk on a network. For a fully connected network we find that the problem can be mapped to the well known coupon collector problem, thus allowing us to estimate form of $P(S,t)$: the distribution…
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
We consider trap models on Z^d, namely continuous time Markov jump process on Z^d with embedded chain given by a generic discrete time random walk, and whose mean waiting time at x is given by tau_x, with tau = (tau_x, x in Z^d) a family of…
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…
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…
A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…
In this study we have carried out computer simulations of random walks on Watts-Strogatz-type small world networks and measured the mean number of visited sites and the return probabilities. These quantities were found to obey scaling…
Activity or spin patterns on random scale-free network are studied by mean field analysis and computer simulations. These activity patterns evolve in time according to local majority-rule dynamics which is implemented using (i) parallel or…
We establish scaling limits for the random walk whose state space is the range of a simple random walk on the four-dimensional integer lattice. These concern the asymptotic behaviour of the graph distance from the origin and the spatial…
Due to wide applications in diverse fields, random walks subject to stochastic resetting have attracted considerable attention in the last decade. In this paper, we study discrete-time random walks on complex network with multiple resetting…
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 study the mechanism behind dynamical trappings experienced during Wang-Landau sampling of continuous systems reported by several authors. Trapping is caused by the random walker coming close to a local energy extremum, although the…
We investigate the trapping problem in Erdos-Renyi (ER) and Scale-Free (SF) networks. We calculate the evolution of the particle density $\rho(t)$ of random walkers in the presence of one or multiple traps with concentration $c$. We show…
We consider one-dimensional discrete-time random walks (RWs) in the presence of finite size traps of length $\ell$ over which the RWs can jump. We study the survival probability of such RWs when the traps are periodically distributed and…
We present an analytical method for computing the mean cover time of a random walk process on arbitrary, complex networks. The cover time is defined as the time a random walker requires to visit every node in the network at least once. This…