The Brownian web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in RÃ—R. We extend the earlier work ofâ€¦ (More)

Let Ï„ = (Ï„i : i âˆˆ Z) denote i.i.d. positive random variables with common distribution F and (conditional on Ï„) let X = (Xt : t â‰¥ 0, X0 = 0), be a continuous-time simple symmetric random walk on Zâ€¦ (More)

We consider a process of two classes of particles jumping on a one-dimensional lattice. The marginal system of the first class of particles is the one-dimensional totally asymmetric simple exclusionâ€¦ (More)

We consider the one dimensional nearest neighbors asymmetric simple exclusion process with rates q and p for left and right jumps respectively; q < p. Ferrari et al. (1991) have shown that if theâ€¦ (More)

Coarsening on a one-dimensional lattice is described by the voter model or equivalently by coalescing (or annihilating) random walks representing the evolving boundaries between regions of constantâ€¦ (More)

We consider a hypersurface of dimension d imbedded in a d + 1 dimensional space. For each x 2 Z d , let t (x) 2 R be the height of the surface at site x at time t. At rate 1 the x-th height isâ€¦ (More)

The Brownian web can be roughly described as a family of coalescing onedimensional Brownian motions starting at all times in R and at all points of R. It was introduced by Arratia; a variant was thenâ€¦ (More)

We consider the position of a tagged particle in the one-dimensional asymmetric nearest-neighbor simple exclusion process. Each particle attempts to jump to the site to its right at rate p and to theâ€¦ (More)

In this paper we construct an object which we call the full Brownian web (FBW) and prove that the collection of all space-time trajectories of a class of one-dimensional stochastic flows convergesâ€¦ (More)

Walking to a pacing stimulus has proven useful in motor rehabilitation, and it has been suggested that spontaneous synchronization could be preferable to intentional synchronization. But it is stillâ€¦ (More)