Related papers: Random walks on randomly evolving graphs
We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…
We investigate a randomly evolving process of subgraphs in an underlying host graph using the spectral theory of semigroups related to the Tsetlin library and hyperplane arrangements. Starting with some initial subgraph, at each iteration,…
The mixer chain on a graph G is the following Markov chain. Place tiles on the vertices of G, each tile labeled by its corresponding vertex. A "mixer" moves randomly on the graph, at each step either moving to a randomly chosen neighbor, or…
We study asymptotic properties of spatially non-homogeneous random walks with non-integrable increments, including transience, almost-sure bounds, and existence and non-existence of moments for first-passage and last-exit times. In our…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
A Random Walk in Changing Environment (RWCE) is a weighted random walk on a locally finite, connected graph $G$ with random, time-dependent edge-weights. This includes self-interacting random walks, where the edge-weights depend on the…
The main paradigm of smoothed analysis on graphs suggests that for any large graph $G$ in a certain class of graphs, perturbing slightly the edges of $G$ at random (usually adding few random edges to $G$) typically results in a graph having…
Given a sequence $(\mathfrak{X}_i, \mathscr{K}_i)_{i=1}^\infty$ of Markov chains, the cut-off phenomenon describes a period of transition to stationarity which is asymptotically lower order than the mixing time. We study mixing times and…
Nodes can be ranked according to their relative importance within the network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based…
In this paper we introduce the notion of Random Walk in Changing Environment - a random walk in which each step is performed in a different graph on the same set of vertices, or more generally, a weighted random walk on the same vertex and…
The mixing behaviour of random walks on lattice points of polytopes using Markov bases is examined. It is shown that under a dilation of the underlying polytope, these random walks do not mix rapidly when a fixed Markov basis is used. We…
We propose an approximation for the first return time distribution of random walks on undirected networks. We combine a message-passing solution with a mean-field approximation, to account for the short- and long-term behaviours…
In this paper, we present a novel approach based on the random walk process for finding meaningful representations of a graph model. Our approach leverages the transient behavior of many short random walks with novel initialization…
Random walks play an important role in probing the structure of complex networks. On traditional networks, they can be used to extract community structure, understand node centrality, perform link prediction, or capture the similarity…
Many seemingly disparate Markov chains are unified when viewed as random walks on the set of chambers of a hyperplane arrangement. These include the Tsetlin library of theoretical computer science and various shuffling schemes. If only…
We investigate the mixing properties of a model of reversible Markov chains in random environment, which notably contains the simple random walk on the superposition of a deterministic graph and a second graph whose vertex set has been…
We develop a model for a random walker with long-range hops on general graphs. This random multi-hopper jumps from a node to any other node in the graph with a probability that decays as a function of the shortest-path distance between the…
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 consider random walks on discrete state spaces, such as general undirected graphs, where the random walkers are designed to approximate a target quantity over the network topology via sampling and neighborhood exploration in the form of…
Establishing cutoff, an abrupt transition from "not mixed" to "well mixed", is a classical topic in the theory of mixing times for Markov chains. Interest has grown recently in determining not only the existence of cutoff and the order of…