Related papers: Deterministic walks in random networks: an applica…

Deterministic tourist walk (DTW) has attracted increasing interest in computer vision. In the last years, different methods for analysis of dynamic and static textures were proposed. So far, all works based on the DTW for texture analysis…

Very recently, a fundamental observable has been introduced and analyzed to quantify the exploration of random walks: the time $\tau_k$ required for a random walk to find a site that it never visited previously, when the walk has already…

We consider random walk on a discrete torus E of side-length N, in sufficiently high dimension d. We investigate the percolative properties of the vacant set corresponding to the collection of sites which have not been visited by the walk…

Several cycle lexicographical orders are found to describe the relative likelihood of elements of the random walks on the symmetric group generated by the conjugacy classes of transpositions, 3-cycles, and n-cycles. Spectral analysis finds…

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…

We introduce a self-organized model of graph evolution associated with preferential network random walkers. The idea is developed by using two different types of walkers, the interactions of which lead to a dynamic graph. The walkers of the…

Owing to their versatility, graph structures admit representations of intricate relationships between the separate entities comprising the data. We formalise the notion of connection between two vertex sets in terms of edge and vertex…

In recent years, computer simulations are playing a fundamental role in unveiling some of the most intriguing features of prime numbers. In this work, we define an algorithm for a deterministic walk through a two-dimensional grid that we…

A thesaurus is one, out of many, possible representations of term (or word) connectivity. The terms of a thesaurus are seen as the nodes and their relationship as the links of a directed graph. The directionality of the links retains all…

Random walks are a common model for exploration and discovery of complex networks. While numerous algorithms have been proposed to map out an unknown network, a complementary question arises: in a known network, which nodes and edges are…

We introduce the concept of a deterministic walk. Confining our attention to the finite state case, we establish hypotheses that ensure that the deterministic walk is transitive, and show that this property is in some sense robust. We also…

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…

We study here the social network generated by the asynchronous visits, to a fixed set of sites, of mobile agents modelled as independent random walks on the plane lattice. The social network is constructed by assuming that a group of agents…

We introduce the concept of a deterministic walk in a deterministic environment on a countable state space (DWDE). For the deterministic walk in a fixed environment we establish properties analogous to those found in Markov chain theory,…

We investigate the relation between the local picture left by the trajectory of a simple random walk on the torus (Z/NZ)^d, d >= 3, until u N^d time steps, u > 0, and the model of random interlacements recently introduced by Sznitman. In…

We give a deterministic, nearly logarithmic-space algorithm that given an undirected graph $G$, a positive integer $r$, and a set $S$ of vertices, approximates the conductance of $S$ in the $r$-step random walk on $G$ to within a factor of…

We introduce a class of generative network models that insert edges by connecting the starting and terminal vertices of a random walk on the network graph. Within the taxonomy of statistical network models, this class is distinguished by…

Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…

Consider a randomly-oriented two dimensional Manhattan lattice where each horizontal line and each vertical line is assigned, once and for all, a random direction by flipping independent and identically distributed coins. A deterministic…

We study the linear large $n$ behavior of the average number of distinct sites $S(n)$ visited by a random walker after $n$ steps on a large random graph. An expression for the graph topology dependent prefactor $B$ in $S(n) = Bn$ is…