Related papers: Traversals of Infinite Graphs with Random Local Or…
In this paper, we present a complete proof of the construction of graphs with bounded valency such that the simple random walk has a return probability at time $n$ at the origin of order $exp(-n^{\alpha}),$ for fixed $\alpha \in [0,1[$ and…
We derive a general formula for computing the expected first return time of a random walk on a finite graph. Using this framework, we calculate the expected first return time in various settings over bounded rectangular grids with different…
Let G be a vertex transitive graph. A study of the range of simple random walk on G and of its bridge is proposed. While it is expected that on a graph of polynomial growth the sizes of the range of the unrestricted random walk and of its…
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…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
We completely characterize when the free effective resistance of an infinite graph can be expressed in terms of simple hitting probabilities of the graphs random walk.
In this paper we develop the idea of Lyons and gives a simple criterion for the recurrence and the transience. We also show that a wedge has the infinite collision property if and only if it is a recurrent graph.
Graphlets are induced subgraph patterns and have been frequently applied to characterize the local topology structures of graphs across various domains, e.g., online social networks (OSNs) and biological networks. Discovering and computing…
Hypergraph has been selected as a powerful candidate for characterizing higher-order networks and has received increasing attention in recent years. In this article, we study random walks with resetting on hypergraph by utilizing spectral…
We study the behavior of Random Walk in Random Environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the ratios of resistances of neighboring edges…
We compute the number of circuits and of loops with multiple crossings in random regular graphs. We discuss the importance of this issue for the validity of the cavity approach. On the one side we obtain analytic results for the infinite…
This paper concerns discrete-time occupancy processes on a finite graph. Our results can be formulated in two theorems, which are stated for vertex processes, but also applied to edge process (e.g., dynamic random graphs). The first theorem…
We provide an explicit algorithm for sampling a uniform simple connected random graph with a given degree sequence. By products of this central result include: (i) continuum scaling limits of uniform simple connected graphs with given…
Topology of urban environments can be represented by means of graphs. We explore the graph representations of several compact urban patterns by random walks. The expected time of recurrence and the expected first passage time to a node…
The Rado graph, also known as the random graph $G(\infty, p)$, is a classical limit object for finite graphs. We study natural ball walks as a way of understanding the geometry of this graph. For the walk started at $i$, we show that order…
Message-passing architectures struggle to sufficiently model long-range dependencies in node and graph prediction tasks. We propose a novel approach exploiting hierarchical graph structures and adaptive random walks to address this…
The lackadaisical quantum walk is a quantum analogue of the lazy random walk obtained by adding a self-loop to each vertex in the graph. We analytically prove that lackadaisical quantum walks can find a unique marked vertex on any regular…
We give upper and lower bounds on the spectral radius of a graph in terms of the number of walks. We generalize a number of known results.
It is shown explicitly how self-similar graphs can be obtained as `blow-up' constructions of finite cell graphs $\hat C$. This yields a larger family of graphs than the graphs obtained by discretising continuous self-similar fractals. For a…
In this expository note, we study several families of periodic graphs which satisfy a sufficient condition for the ergodicity of the associated continuous-time quantum walk. For these graphs, we compute the limiting distribution of the walk…