In the bootstrap percolation model, sites in an L by L square are initially independently declared active with probability p. At each time step, an inactive site becomes active if at least two of itsâ€¦ (More)

Let Î be an ergodic simple point process on R and let Î be its Palm version. Thorisson [Ann. Probab. 24 (1996) 2057â€“2064] proved that there exists a shift coupling of Î and Î ; that is, one can selectâ€¦ (More)

We give a rigorous and self-contained survey of the abelian sandpile model and rotor-router model on finite directed graphs, highlighting the connections between them. We present several intriguingâ€¦ (More)

Let Îž be a discrete set in Rd. Call the elements of Îž centers. The well-known Voronoi tessellation partitions Rd into polyhedral regions (of varying sizes) by allocating each site of Rd to theâ€¦ (More)

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,â€¦ (More)

A factor graph of a point process is a graph whose vertices are the points of the process, and which is constructed from the process in a deterministic isometry-invariant way. We prove that theâ€¦ (More)

We propose a new approach to edge bundling. The approach starts by routing the edge paths to minimize a weighted sum of the total length of the paths together with the ink required to draw them. Asâ€¦ (More)

We study a variant of bootstrap percolation in which growth is restricted to a single active cluster. Initially there is a single active site at the origin, while other sites of Z are independentlyâ€¦ (More)