Related papers: Deterministic walks in random networks: an applica…
Deterministic walks over a random set of points in one and two dimensions (d=1,2) are considered. Points (``cities'') are randomly scattered in R^d following a uniform distribution. A walker (a ``tourist''), at each time step, goes to the…
Consider a medium characterized by N points whose coordinates are randomly generated by a uniform distribution along the edges of a unitary d-dimensional hypercube. A walker leaves from each point of this disordered medium and moves…
Consider a random medium consisting of points randomly distributed so that there is no correlation among the distances. This is the random link model, which is the high dimensionality limit (mean field approximation) for the euclidean…
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,…
We study the properties of discrete-time random walks on networks formed by randomly interconnected cliques, namely, random networks of cliques. Our purpose is to derive the parameters that define the network structure -- specifically, the…
The set of visited sites and the number of visited sites are two basic properties of the random walk trajectory. We consider two independent random walks on a hyper-cubic lattice and study ordering probabilities associated with these…
We consider a mortal random walker on a family of hierarchical graphs in the presence of some trap sites. The configuration comprising the graph, the starting point of the walk, and the locations of the trap sites is taken to be exactly…
We consider the problem of traveling among random points in Euclidean space, when only a random fraction of the pairs are joined by traversable connections. In particular, we show a threshold for a pair of points to be connected by a…
Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These…
Suppose that the vertices of the Euclidean lattice Z^d are endowed with a random scenery, obtained by tossing a fair coin at each vertex. A random walker, starting from the origin, replaces the coins along its path by i.i.d. biased coins.…
We revisit an old minor topic in algorithms, the deterministic walk on a finite graph which always moves toward the nearest unvisited vertex until every vertex is visited. There is an elementary connection between this cover time and…
We consider random walks on dynamical networks where edges appear and disappear during finite time intervals. The process is grounded on three independent stochastic processes determining the walker's waiting-time, the up-time and down-time…
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.…
Consider the following computational problem: given a regular digraph $G=(V,E)$, two vertices $u,v \in V$, and a walk length $t\in \mathbb{N}$, estimate the probability that a random walk of length $t$ from $u$ ends at $v$ to within $\pm…
We find that a symbolic walk (performed by a walker with memory given by a Bernoulli shift) is able to distinguish between the random or chaotic topology of a given network. We show this result by means of studying the undirected baker…
Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the…
Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill. First--passage time…
Random walks by single-node agents have been systematically conducted on various types of complex networks in order to investigate how their topologies can affect the dynamics of the agents. However, by fitting any network node, these…
This paper introduces nondeterministic walks, a new variant of one-dimensional discrete walks. The main difference to classical walks is that its nondeterministic steps consist of sets of steps from a predefined set such that all possible…
Random walks on discrete lattices are fundamental models that form the basis for our understanding of transport and diffusion processes. For a single random walker on complex networks, many properties such as the mean first passage time and…