Rate of Escape of the Mixer Chain
Probability
2009-01-13 v2 Group Theory
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 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.
Cite
@article{arxiv.math/0506129,
title = {Rate of Escape of the Mixer Chain},
author = {Ariel Yadin},
journal= {arXiv preprint arXiv:math/0506129},
year = {2009}
}