Related papers: The Meeting Time of Multiple Random Walks

Coalescing random walks is a fundamental stochastic process, where a set of particles perform independent discrete-time random walks on an undirected graph. Whenever two or more particles meet at a given node, they merge and continue as a…

Mixing of finite time-homogeneous Markov chains is well understood nowadays, with a rich set of techniques to estimate their mixing time. In this paper, we study the mixing time of random walks in dynamic random environments. To that end,…

We analyse the problem of meeting times for interdependent stochastic agents: random walkers whose behaviour is stochastic but controlled by their selections from some set of allowed actions, and the inference problem of when these agents…

We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time…

We study the linear large $n$ behavior of the average number of distinct sites $S(n)$ visited by a random walker after $n$ steps on a large random graph. An expression for the graph topology dependent prefactor $B$ in $S(n) = Bn$ is…

A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…

The expected meeting time of two random walkers on an undirected graph of size $N$, where at each time step one walker moves and the process stops when they collide, satisfies a system of $\binom{N}{2}$ linear equations. Na\"{i}vely,…

We experimentally demonstrate that the statistical properties of distances between pedestrians which are hindered from avoiding each other are described by the Gaussian Unitary Ensemble of random matrices. The same result has recently been…

This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with…

We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…

We examine the mixing time for random walks on graphs. In particular we are interested on investigating graphs with bottlenecks. Furthermore, the cutoff phenomenon is examined.

The statistics of first-passage times of random walks to target sites has proved to play a key role in determining the kinetics of space exploration in various contexts. In parallel, the number of distinct sites visited by a random walker…

Given a finite graph G, a vertex of the lamplighter graph consists of a zero-one labeling of the vertices of G, and a marked vertex of G. For transitive graphs G, we show that, up to constants, the relaxation time for simple random walk in…

In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We perform extensive simulations for the calculation of the mean squared displacement, the network coverage and the…

A coupling of random walkers on the same finite graph, who take turns sequentially, is said to be an avoidance coupling if the walkers never collide. Previous studies of these processes have focused almost exclusively on complete graphs, in…

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…

The rotor walk is a derandomized version of the random walk on a graph. On successive visits to any given vertex, the walker is routed to each of the neighboring vertices in some fixed cyclic order, rather than to a random sequence of…

We consider random walks on dynamical networks where edges appear and disappear during finite time intervals. The process is grounded on three independent stochastic processes determining the walker's waiting-time, the up-time and down-time…

We address the correspondence search problem among multiple graphs with complex properties while considering the matching consistency. We describe each pair of graphs by combining multiple attributes, then jointly match them in a unified…

Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…