Open Access
2009 Rate of Escape of the Mixer Chain
Ariel Yadin
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Electron. Commun. Probab. 14: 347-357 (2009). DOI: 10.1214/ECP.v14-1474


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 $t$.


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Ariel Yadin. "Rate of Escape of the Mixer Chain." Electron. Commun. Probab. 14 347 - 357, 2009.


Accepted: 26 August 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1190.60064
MathSciNet: MR2535083
Digital Object Identifier: 10.1214/ECP.v14-1474

Primary: 60J10
Secondary: 60B15

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