Random monotone paths on polyhedra
Günter M. Ziegler · 2004
Consider the following simple random process, on a 3-dimensional bounded convex polyhedron, with a given starting vertex: Repeatedly choose a random edge that goes "down" (decreasing the z-coordinate), and follow it to the vertex at the other end -- if there are several choices, pick one of them, with equal probability. Stop once you have reached a vertex with minimal z-coordinate.