Related papers: Cutoff for random walk on random graphs with a com…

A comparison technique for finite random walks on finite graphs is introduced, using the well-known interlacing method. It yields improved return probability bounds. A key feature is the incorporation of parts of the spectrum of the…

Motivated by an application in community detection, we consider an \ER random graph conditioned on the rare event that all connected components are fully connected. Such graphs can be considered as partitions of vertices into cliques.…

We give conditions under which near-critical stochastic processes on the half-line have infinitely many or finitely many cutpoints, generalizing existing results on nearest-neighbour random walks to adapted processes with bounded increments…

In the book [FIM], original methods were proposed to determine the invariant measure of random walks in the quarter plane with small jumps, the general solution being obtained via reduction to boundary value problems. Among other things, an…

We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity {\gamma} is defined. Our data consists in a sequence of partial observations of a fractional random walk on G. The observations are partial…

The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph.…

This article introduces a model for interacting vertex-reinforced random walks, each taking values on a complete sub-graph of a locally finite undirected graph. The transition probability for a walk to a given vertex depends on the…

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…

In this article, we consider products of random walks on finite groups with moderate growth and discuss their cutoffs in the total variation. Based on several comparison techniques, we are able to identify the total variation cutoff of…

Random walks on graphs can be slow. To speed them up, imagine that at each step instead of choosing the neighbor at random, there is a small probability $\varepsilon>0$ that we can choose it. We show that in this case, at least for graphs…

The node2vec random walk is a non-Markovian random walk on the vertex set of a graph, widely used for network embedding and exploration. This random walk model is defined in terms of three parameters which control the probability of,…

In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…

In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The…

We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…

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…

In this paper we prove a rate of escape theorem and a central limit theorem for isotropic random walks on Fuchsian buildings, giving formulae for the speed and asymptotic variance. In particular, these results apply to random walks induced…

Discovered in the context of card shuffling by Aldous, Diaconis and Shahshahani, the cutoff phenomenon has since then been established in a variety of Markov chains. However, proving cutoff remains a delicate affair, which requires a…

We present a simple and flexible method to prove consistency of semidefinite optimization problems on random graphs. The method is based on Grothendieck's inequality. Unlike the previous uses of this inequality that lead to constant…

We prove a general theorem on cutoffs for symmetric simple exclusion processes on graphs with open boundaries, under the natural assumption that the graphs converge geometrically and spectrally to a compact metric measure space with…

We show how to construct discrete-time quantum walks on directed, Eulerian graphs. These graphs have tails on which the particle making the walk propagates freely, and this makes it possible to analyze the walks in terms of scattering…