The University of Michigan Combinatorics Seminar
Hypersimplices are the slices of cubes perpendicular to the
vector (1,1, ... ,1). The problem of computing a mixed volume
involving these polytopes turns out to be equivalent to
computing the probability that a certain random walk of many
points on a circle ends up in a particular position.
This enables one to compute many of these mixed volumes quickly.
Any mixed volume of polytopes can be phrased in this way but
in general will lead to a random walk in a larger space and
with many final positions instead of just one.