Related papers: Random walks on dynamical percolation: mixing time…
Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an…
Simple random walks on a partially directed version of $\mathbb{Z}^2$ are considered. More precisely, vertical edges between neighbouring vertices of $\mathbb{Z}^2$ can be traversed in both directions (they are undirected) while horizontal…
We study the asymptotic behavior of the simple random walk on oriented versions of $\mathbb{Z}^2$. The considered lattices are not directed on the vertical axis but unidirectional on the horizontal one, with random orientations whose…
We study biased random walks on dynamical percolation on $\mathbb{Z}^d$. We establish a law of large numbers and an invariance principle for the random walk using regeneration times. Moreover, we verify that the Einstein relation holds, and…
The scaling properties of a random walker subject to the global constraint that it needs to visit each site an even number of times are determined. Such walks are realized in the equilibrium state of one dimensional surfaces that are…
We study the mean traversal time for a class of random walks on Newman-Watts small-world networks, in which steps around the edge of the network occur with a transition rate F that is different from the rate f for steps across small-world…
We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds ($F$) and…
Theoretical analysis of random walk on percolation lattices has predicted that, at the occupied site concentrations of above the threshold value, a characteristic crossover between an initial sub-diffusion to a final classical diffusion…
In the randomly-oriented Manhattan lattice, every line in $\mathbb{Z}^d$ is assigned a uniform random direction. We consider the directed graph whose vertex set is $\mathbb{Z}^d$ and whose edges connect nearest neighbours, but only in the…
Random walks on expanders play a crucial role in Markov Chain Monte Carlo algorithms, derandomization, graph theory, and distributed computing. A desirable property is that they are rapidly mixing, which is equivalent to having a spectral…
We study the time evolution of continuous-time quantum walks on randomly changing graphs. At certain moments edges of the graph appear or disappear with a given probability. We focus on the case when the time interval between subsequent…
We give an explicit formula for the mean square displacement of the random walk on the $d$-dimensional Manhattan lattice after $n$ steps, for all $n$ and all dimensions $d \geq 2$.
We study random walks evolving in continuous time on a one-dimensional lattice where each site $x$ hosts a quenched random potential $U_x$. The potentials on different sites are independent, identically distributed Gaussian random…
The rotor router model is a popular deterministic analogue of a random walk on a graph. Instead of moving to a random neighbor, the neighbors are served in a fixed order. We examine how fast this "deterministic random walk" covers all…
We consider one or more independent random walks on the $d\ge 3$ dimensional discrete torus. The walks start from vertices chosen independently and uniformly at random. We analyze the fluctuation behavior of the size of some random sets…
This investigation is motivated by a result we proved recently for the random transposition random walk: the distance from the starting point of the walk has a phase transition from a linear regime to a sublinear regime at time $n/2$. Here,…
The intersecting pedestrian flow on the 2D lattice with random update rule is studied. Each pedestrian has three moving directions without the back step. Under periodic boundary conditions, an intermediate phase has been found at which some…
We explore some of the connections between the local picture left by the trace of simple random walk on a discrete cylinder with base a d-dimensional torus, d at least 2, of side-length N running for times of order N^{2d} and the model of…
Assign to each vertex of the one-dimensional torus i.i.d. weights with a heavy-tail of index $\tau-1>0$. Connect then each couple of vertices with probability roughly proportional to the product of their weights and that decays polynomially…
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…