@article{ECP1474,
author = {Ariel Yadin},
title = {Rate of Escape of the Mixer Chain},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {14},
year = {2009},
keywords = {},
abstract = {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 $\mathbb{Z}$, 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 $t$.},
pages = {no. 35, 347-357},
issn = {1083-589X},
doi = {10.1214/ECP.v14-1474},
url = {http://ecp.ejpecp.org/article/view/1474}}