Interlacements and the Wired Uniform Spanning Forest

  title={Interlacements and the Wired Uniform Spanning Forest},
  author={TOM HUTCHCROFT},
  • Published 2015
We extend the Aldous-Broder algorithm to generate the wired uniform spanning forests (WUSFs) of infinite, transient graphs. We do this by replacing the simple random walk in the classical algorithm with Sznitman’s random interlacement process. We then apply this algorithm to study the WUSF, showing that every component of the WUSF is one-ended almost surely in any graph satisfying a certain weak anchored isoperimetric condition, that the number of ‘excessive ends’ in the WUSF is non-random in… CONTINUE READING