We consider a random object that is associated with both random walks and random media, specifically, the superposition of a configuration of subcritical Bernoulli percolation on an infinite connected ...

Lawler, Schramm and Werner showed that the scaling limit of the loop-erased random walk on ℤ 2 is SLE 2 . We consider scaling limits of the loop-erasure of random walks on other planar graphs (graphs ...

In algorithms, as in life, negativity can be a drag. Consider the problem of finding the shortest path between two points on a graph — a network of nodes connected by links, or edges. Often, these ...