We consider a random walk on the discrete cylinder (Z/NZ)d×Z, d ≥ 3 with drift N−dα in the Z-direction and investigate the large N -behavior of the disconnection time T disc N , defined as the first time when the trajectory of the random walk disconnects the cylinder into two infinite components. We prove that, as long as the drift exponent α is strictly greater than 1, the asymptotic behavior ...

We study the localization of probability distribution in a discrete quantum random walk on an infinite chain. With a phase defect introduced in any position of the quantum random walk (QRW), we have found that the localization of the probability distribution in the QRW emerges. Different localized behaviors of the probability distribution in the QRW are presented when the defect occupies differ...

The well-scaled transition to the diffusion limit in the framework of the theory of continuous-time random walk (CTRW) is presented starting from its representation as an infinite series that points out the subordinated character of the CTRW itself. We treat the CTRW as a combination of a random walk on the axis of physical time with a random walk in space, both walks happening in discrete oper...

This paper exploits the properties of the commute time to develop a graphspectral method for image segmentation. Our starting point is the lazy random walk on the graph, which is determined by the heat-kernel of the graph and can be computed from the spectrum of the graph Laplacian. We characterise the random walk using the commute time between nodes, and show how this quantity may be computed ...

This paper designs a numerical procedure to price discrete Euro-pean barrier options in Black-Scholes model. The pricing problem is divided in a series of initial value problems, one for each monitoring time. Each initial value problem is solved by replacing the driving Brownian motion by a lattice random walk. Some results from the theory of Besov spaces will be presented which show that the c...

We outline a strategy for showing convergence of loop-erased random walk on the Z square lattice to SLE(2), in the supremum norm topology that takes the time parametrization of the curves into account. The discrete curves are parametrized so that the walker moves at a constant speed determined by the lattice spacing, and the SLE(2) curve has the recently introduced natural time parametrization....

In a coalescing random walk, a set of particles make independent discrete-time random walks on a graph. Whenever one or more particles meet at a vertex, they unite to form a single particle, which then continues a random walk through the graph. Let G = (V,E), be an undirected and connected graph, with n vertices and m edges. The coalescence time, C(n), is the expected time for all particles to ...

Abstract. We consider a simple random walk on a discrete torus (Z/NZ) with dimension d ≥ 3 and large side length N . For a fixed constant u ≥ 0, we study the percolative properties of the vacant set, consisting of the set of vertices not visited by the random walk in its first [uN] steps. We prove the existence of two distinct phases of the vacant set in the following sense: if u > 0 is chosen ...