Related papers: Random walks on complex networks with first-passag…
Sood and Grassberger studied in [Phys. Rev. Lett. 99, 098701 (2007)] random walks on random graphs that are biased towards a fixed target point. They put forward a critical bias strength b_c such that a random walker on an infinite graph…
We investigate the dynamics of random walks on weighted networks. Assuming that the edge's weight and the node's strength are used as local information by a random walker, we study two kinds of walks, weight-dependent walk and…
The cost of stochastic resetting is considered within the context of a discrete random walk model. In addition to standard stochastic resetting, for which a reset occurs with a certain probability after \emph{each} step, we introduce a…
We consider biased random walks on random networks constituted by a random comb comprising a backbone with quenched-disordered random-length branches. The backbone and the branches run in the direction of the bias. For the bare model as…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
In this paper, we investigate random walk based token circulation in dynamic environments subject to failures. We describe hypotheses on the dynamic environment that allow random walks to meet the important property that the token visits…
The random walk with choice is a well known variation to the random walk that first selects a subset of $d$ neighbours nodes and then decides to move to the node which maximizes the value of a certain metric; this metric captures the number…
A powerful strategy to accelerate quantum-walk-based search algorithms leverages on resetting protocols, where a detector monitors a target site and the evolution of the walker is restarted if no detection occurs within a fixed time…
Analytical results for the distribution of first hitting times of random walks on Erd\H{o}s-R\'enyi networks are presented. Starting from a random initial node, a random walker hops between adjacent nodes until it hits a node which it has…
The cover-time problem, i.e., time to visit every site in a system, is one of the key issues of random walks with wide applications in natural, social, and engineered systems. Addressing the full distribution of cover times for random walk…
The statistics of first-passage times of random walks to target sites has proved to play a key role in determining the kinetics of space exploration in various contexts. In parallel, the number of distinct sites visited by a random walker…
Random walk on the set of irreducible representations of a finite group is investigated. For the symmetric and general linear groups, a sharp convergence rate bound is obtained and a cutoff phenomenon is proved. As related results, an…
The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…
For random walks on networks (graphs), it is a theoretical challenge to explicitly determine the mean first-passage time (MFPT) between two nodes averaged over all pairs. In this paper, we study the MFPT of random walks in the famous…
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…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
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…
We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds ($F$) and…
We study a discrete random walk on a one-dimensional finite lattice, where each state has different probabilities to move one step forward, backward, staying for a moment or being absorbed. We obtain expected number of arrivals and expected…