Related papers: Continuous-time vertex-reinforced random walks on …
In this paper, we are interested in the mixing behaviour of simple random walks on inhomogeneous directed graphs. We focus our study on the Chung-Lu digraph, which is an inhomogeneous network that generalizes the Erd\H{o}s-R\'enyi digraph.…
We introduce a technique using nonbacktracking random walk for estimating the spectral radius of simple random walk. This technique relates the density of nontrivial cycles in simple random walk to that in nonbacktracking random walk. We…
We study financial distributions within the framework of the continuous time random walk (CTRW). We review earlier approaches and present new results related to overnight effects as well as the generalization of the formalism which embodies…
We consider a random object that is associated with both random walks and random media, specifically, the superposition of a configuration of subcritical Bernoulli percolation on an infinite connected graph and the trace of the simple…
The Semi-Markov property of Continuous Time Random Walks (CTRWs) and their limit processes is utilized, and the probability distributions of the bivariate Markov process $(X(t),V(t))$ are calculated: $X(t)$ is a CTRW limit and $V(t)$ a…
It is shown that the path of a simple random walk on any graph, consisting of all vertices visited and edges crossed by the walk, is almost surely a recurrent subgraph.
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…
Continuous-time random walk (CTRW) is a model of anomalous sub-diffusion in which particles are immobilized for random times between successive jumps. A power-law distribution of the waiting times, $\psi(\tau) \tau^{-(1+\alpha)}$, leads to…
We review various features of the statistics of random paths on graphs. The relationship between path statistics and Quantum Mechanics (QM) leads to two canonical ways of defining random walk on a graph, which have different statistics and…
Let G be a quasirandom graph on n vertices, and let W be a random walk on G of length alpha n^2. Must the set of edges traversed by W form a quasirandom graph? This question was asked by B\"ottcher, Hladk\'y, Piguet and Taraz. Our aim in…
We analyze greedy routing in a random graph G_n constructed on the vertex set V = {1, 2, ..., n} embedded in Z. Vertices are inserted according to a uniform random permutation pi, and each newly inserted vertex connects to its nearest…
. In this paper we give a survey of some recent results for random walk in random scenery (RWRS). On $\mathbb {Z}^d$, $d\geq 1$, we are given a random walk with i.i.d. increments and a random scenery with i.i.d. components. The walk and the…
We consider the possible visits to visible points of a random walker moving up and right in the integer lattice (with probability $\alpha$ and $1-\alpha$, respectively) and starting from the origin. We show that, almost surely, the…
Functional limit theorem for continuous-time random walks (CTRW) are found in general case of dependent waiting times and jump sizes that are also position dependent. The limiting anomalous diffusion is described in terms of fractional…
This Master's thesis examines the properties of large degree vertices in random recursive directed acyclic graphs (RRDAGs), a generalization of the well-studied random recursive tree (RRT) model. Using a novel adaptation of Kingman's…
A close relation between hitting times of the simple random walk on a graph, the Kirchhoff index, resistance-centrality, and related invariants of unicyclic graphs is displayed. Combining with the graph transformations and some other…
In this article, we study a simple random walk on a decorated Galton-Watson tree, obtained from a Galton-Watson tree by replacing each vertex of degree $n$ with an independent copy of a graph $G_n$ and gluing the inserted graphs along the…
We define here a \textit{directed edge reinforced random walk} on a connected locally finite graph. As the name suggests, this walk keeps track of its past, and gives a bias towards directed edges previously crossed proportional to the…
The mixing time of a random walk, with or without backtracking, on a random graph generated according to the configuration model on $n$ vertices, is known to be of order $\log n$. In this paper we investigate what happens when the random…
Let $P$ be an irreducible and reversible transition matrix on a finite state space $V$ with invariant distribution $\pi$. We let $k$ chains start by choosing independent locations distributed according to $\pi$ and then they evolve…