Spanning trees of graphs on surfaces and the intensity of loop-erased random walk on planar graphs

  title={Spanning trees of graphs on surfaces and the intensity of loop-erased random walk on planar graphs},
  author={Richard W. Kenyon and D. Wilson},
  journal={Journal of the American Mathematical Society},
  • Richard W. Kenyon, D. Wilson
  • Published 2014
  • Mathematics
  • Journal of the American Mathematical Society
  • We show how to compute the probabilities of various connection topologies for uniformly random spanning trees on graphs embedded in surfaces. As an application, we show how to compute the "intensity" of the loop-erased random walk in ${\mathbb Z}^2$, that is, the probability that the walk from (0,0) to infinity passes through a given vertex or edge. For example, the probability that it passes through (1,0) is 5/16; this confirms a conjecture from 1994 about the stationary sandpile density on… CONTINUE READING
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