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

We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogenous random walks in the plane which interlace two…

This paper proposes a random walk model to analyze visitors' mobility patterns in a large museum. Visitors' available time makes their visiting styles different, resulting in dissimilarity in the order and number of visited places and in…

Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various timescales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis…

This study introduces an algorithm that generates undirected graphs with three main characteristics of real-world networks: scale-freeness, short distances between nodes (small-world phenomenon), and large clustering coefficients. The main…

Motivated by a problem arising from pharmaceutical science [B. Baeumer et al., Discr. Contin. Dyn. Sys. B 12], we study random walks on the contact graph of a bidisperse random sphere packing. For a random walk on the unweighted graph that…

In this paper we explore the features of a graph generated by random walkers with nodes that have evolutionary attractiveness and Boltzmann-like transition probabilities that depend both on the euclidean distance between the nodes and on…

For any pseudo-Anosov diffeomorphism on a closed orientable surface $S$ of genus greater than one, it is known by the work of Bers and Thurston that the topological entropy agrees with the translation distance on the Teichm\"uller space…

Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…

A self-repelling random walk of a token on a graph is one in which at each step, the token moves to a neighbor that has been visited least often (with ties broken randomly). The properties of self-repelling random walks have been analyzed…

Consider a collaborative dynamic of $k$ independent random walks on a finite connected graph $G$. We are interested in the size of the set of vertices visited by at least one walker and study how the number of walkers relates to the…

For a symmetric random walk in $Z^2$ which does not necessarily have bounded jumps we study those points which are visited an unusually large number of times. We prove the analogue of the Erd\H{o}s-Taylor conjecture and obtain the…

We base ourselves on the construction of the two-dimensional random interlacements [12] to define the one-dimensional version of the process. For this constructions we consider simple random walks conditioned on never hitting the origin,…

We consider the problem of assigning appearing times to the edges of a digraph in order to maximize the (average) temporal reachability between pairs of nodes. Motivated by the application to public transit networks, where edges cannot be…

Focusing on coupling between edges, we generalize the relationship between the normalized graph Laplacian and random walks on graphs by devising an appropriate normalization for the Hodge Laplacian -- the generalization of the graph…

We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…

We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…

For $\lambda>0$, we define a $\lambda$-damped random walk to be a random walk that is started from a random vertex of a graph and stopped at each step with probability $\frac{\lambda}{1+\lambda}$, otherwise continued with probability…

An Euler tour of a hypergraph is a closed walk that traverses every edge exactly once; if a hypergraph admits such a walk, then it is called eulerian. Although this notion is one of the progenitors of graph theory --- dating back to the…

Consider a simple graph in which a random walk begins at a given vertex. It moves at each step with equal probability to any neighbor of its current vertex, and ends when it has visited every vertex. We call such a random walk a random…

We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…