Rate of escape of the mixer chain

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 t3/4, up to constants. This is a new example of a random walk on a group with rate of escape strictly between t1/2 and t.

Original languageEnglish
Pages (from-to)347-357
Number of pages11
JournalElectronic Communications in Probability
StatePublished - 1 Jan 2009
Externally publishedYes


  • Random walks

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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