Related papers: Non-backtracking random walks mix faster

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…

We consider a random geometric graph obtained by placing a Poisson point process of intensity 1 in the d-dimensional torus of side length n^(1/d) and connecting two points by an edge if their distance is at most r. We consider the case of…

We establish conditions on sequences of graphs which ensure that the mixing times of the random walks on the graphs in the sequence converge. The main assumption is that the graphs, associated measures and heat kernels converge in a…

We study analytically a simple random walk model on a one-dimensional lattice, where at each time step the walker resets to the maximum of the already visited positions (to the rightmost visited site) with a probability $r$, and with…

We study the set of probability distributions visited by a continuous-time quantum walk on graphs. An edge-weighted graph G is universal mixing if the instantaneous or average probability distribution of the quantum walk on G ranges over…

Kemeny's constant for a connected graph $G$ is the expected time for a random walk to reach a randomly-chosen vertex $u$, regardless of the choice of the initial vertex. We extend the definition of Kemeny's constant to non-backtracking…

We introduce a Markov chain for sampling from the uniform distribution on a Riemannian manifold $\mathcal{M}$, which we call the $\textit{geodesic walk}$. We prove that the mixing time of this walk on any manifold with positive sectional…

Researchers have designed many algorithms to measure the distances between graph nodes, such as average hitting times of random walks, cosine distances from DeepWalk, personalized PageRank, etc. Successful although these algorithms are,…

Random walks on graphs are an essential primitive for many randomised algorithms and stochastic processes. It is natural to ask how much can be gained by running $k$ multiple random walks independently and in parallel. Although the cover…

We introduce the continuous-time vertex-reinforced random walk (cVRRW) as a continuous-time version of the vertex-reinforced random walk (VRRW), which might open a new perspective on the study of the VRRW. It has been proved by Limic and…

We introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to…

Given a connected graph $G$ with some subset of its vertices excited and a fixed target vertex, in the geodesic-biased random walk on $G$, a random walker moves as follows: from an unexcited vertex, she moves to a uniformly random…

This paper focuses on the problem of modeling for small world effect on complex networks. Let's consider the supercritical Poisson continuous percolation on $d$-dimensional torus $T^d_n$ with volume $n^d$. By adding "long edges (short…

The $N$-step random walk, elongated in the vicinity of a disc (in 2D) or a sphere (in 3D) of radius $R$, demonstrates a non-algebraic stretched exponential decay $P_N\sim \exp\left(-{\rm const}\, N^{1/3}\right)$ for the first return…

Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…

We analyse a random walk on the ring of integers mod $n$, which at each time point can make an additive `step' or a multiplicative `jump'. When the probability of making a jump tends to zero as an appropriate power of $n$ we prove the…

We study the mixing time of a random walk on the torus, alternated with a Lebesgue measure preserving Bernoulli map. Without the Bernoulli map, the mixing time of the random walk alone is $O(1/\epsilon^2)$, where $\epsilon$ is the step…

Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…

We introduce a general class of random walks on the $N$-hypercube, study cut-off for the mixing time, and provide several types of representation for the transition probabilities. We observe that for a sub-class of these processes with long…

An algorithm observes the trajectories of random walks over an unknown graph $G$, starting from the same vertex $x$, as well as the degrees along the trajectories. For all finite connected graphs, one can estimate the number of edges $m$ up…