Related papers: An electric-resistance approach to return time
Consider a random walk on a tree $G=(V,E)$. For $v,w \in V$, let the hitting time $H(v,w)$ denote the expected number of steps required for the random walk started at $v$ to reach $w$, and let $\pi_v = \mathrm{deg}(v)/2|E|$ denote the…
Various graph algorithms have been developed with multiple random walks, the movement of several independent random walkers on a graph. Designing an efficient graph algorithm based on multiple random walks requires investigating multiple…
We define a random walk problem which admits analytic results, on a class of infinite periodic lattices which are directed and colored. Our approach is motivated from the fact that such lattices arise in string theoretic constructs of…
Previous work has shown the effectiveness of random walk hitting times as a measure of dissimilarity in a variety of graph-based learning problems such as collaborative filtering, query suggestion or finding paraphrases. However,…
We consider the range of random walks up to time n, R_n, on graphs satisfying a uniform condition. This condition is characterized by potential theory. Not only all vertex transitive graphs but also many non-regular graphs satisfy the…
We consider the problem of estimating the expected time to find a maximum degree node on a graph using a (parameterized) biased random walk. For assortative graphs the positive degree correlation serves as a local gradient for which a bias…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…
In this paper we study the distribution of hitting and return times for observations of dynamical systems. We apply this results to get an exponential law for the distribution of hitting and return times for rapidly mixing random dynamical…
We analyze the covertime of a biased random walk on the random graph $G_{n,p}$. The walk is biased towards visiting vertices of low degree and this makes the covertime less than in the unbiased case
In this article, universal concentration estimates are established for the local times of random walks on weighted graphs in terms of the resistance metric. As a particular application of these, a modulus of continuity for local times is…
We introduce and simulate the random walk that adapts move strategies according to local node preferences on a directed graph. We consider graphs with double-hierarchical connectivity and variable wiring diagram in the universality class of…
Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a…
We demonstrate a quantum walk with time-dependent coin bias. With this technique we realize an experimental single-photon one-dimensional quantum walk with a linearly-ramped time-dependent coin flip operation and thereby demonstrate two…
We present an easy proof of Polya's theorem on random walks: with the probability one a random walk on the two-dimensional lattice returns to the starting point.
This is a review article on the distributions of entry and return times in dynamical systems which discusses recent results for systems of positive entropy.
We show that the expected time for a random walk on a (multi-)graph $G$ to traverse all $m$ edges of $G$, and return to its starting point, is at most $2m^2$; if each edge must be traversed in both directions, the bound is $3m^2$. Both…
In this article we consider resistance matrix of a connected graph. For unweighted graph we study some necessary and sufficient conditions for resistance regular graphs. Also we find some relationship between Laplacian matrix and resistance…
We introduce a new type of random walk where the definition of edge reinforcement is very different from the one in the reinforced random walk models studied so far, and investigate its basic properties, such as null/positive recurrence,…
We investigate unimodular random networks. Our motivations include their characterization via reversibility of an associated random walk and their similarities to unimodular quasi-transitive graphs. We extend various theorems concerning…
We investigate the behavior of electric potentials on distance-regular graphs, and extend some results of a prior paper. Our main result, Theorem 4, shows(together with Corollary 3) that if distance is measured by the electric resistance…