  The mixer chain on a graph G is the following Markov chain. Place tiles on
the vertices of G, each tile labeled by its corresponding vertex. A "mixer"
moves randomly on the graph, at each step either moving to a randomly chosen
neighbor, or swapping the tile at its current position with some randomly
chosen adjacent tile.
  We study the mixer chain on Z, and show that at time t the expected distance
to the origin is t^{3/4}, up to constants. This is a new example of a random
walk on a group with rate of escape strictly between t^{1/2} and t.
