Related papers: Topological and Geometrical Random Walks on Bidisp…
In this paper, we introduce random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension $d$, a random walk with an absorbing state is defined which relates to the spectrum of the $k$-dimensional…
We propose random walks on suitably defined graphs as a framework for finescale modeling of particle motion in an obstructed environment where the particle may have interactions with the obstructions and the mean path length of the particle…
We introduce a set of techniques that allow for efficiently generating many independent random walks in the Massive Parallel Computation (MPC) model with space per machine strongly sublinear in the number of vertices. In this…
We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…
We show that anomalous diffusion can result when the steps of a random walk are not statistically independent. We present an algorithm that counts all the possible paths of particles diffusing on random graphs with arbitrary degree…
Graph clustering is an important technique to understand the relationships between the vertices in a big graph. In this paper, we propose a novel random-walk-based graph clustering method. The proposed method restricts the reach of the…
In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We perform extensive simulations for the calculation of the mean squared displacement, the network coverage and the…
The range, local times, and periodicity of symmetric, weakly asymmetric and asymmetric random walks at the time of exit from a strip with $N$ locations are considered. Several results on asymptotic distributions are obtained.
We introduce the notion of a "random basic walk" on an infinite graph, give numerous examples, list potential applications, and provide detailed comparisons between the random basic walk and existing generalizations of simple random walks.…
We present an algorithm to grow a graph with scale-free structure of {\it in-} and {\it out-links} and variable wiring diagram in the class of the world-wide Web. We then explore the graph by intentional random walks using local…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
In this note, we try to analyze and clarify the intriguing interplay between some counting problems related to specific thermalized weighted graphs and random walks consistent with such graphs.
We study the set of directions asymptotically explored by a spatially homogeneous random walk in $d$-dimensional Euclidean space. We survey some pertinent results of Kesten and Erickson, make some further observations, and present some…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric…
We investigate crossing path probabilities for two agents that move randomly in a bounded region of the plane or on a sphere (denoted $R$). At each discrete time-step the agents move, independently, fixed distances $d_1$ and $d_2$ at angles…
We study the graph-theoretic properties of the trace of random walks on pseudorandom graphs. We show that for any $\varepsilon>0$, there exists a constant $C$ such that the cover time of an $(n,d,\lambda)$-graph $G$ with $d/\lambda\ge C$ is…
The study of matter fields on an ensemble of random geometries is a difficult problem still in need of new methods and ideas. We will follow a point of view inspired by probability theory techniques that relies on an expansion of the two…
Random walks on graphs are a fundamental concept in graph theory and play a crucial role in solving a wide range of theoretical and applied problems in discrete math, probability, theoretical computer science, network science, and machine…
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…