Wilson, David B.
- Working Paper
We give a simple formula for the loop-erased random walk looping rate of a finite planar graph. The looping rate is closely related to the expected amount of sand in a recurrent sandpile on the graph. The looping rate formula is well-suited to taking limits where the graph tends to an infinite lattice, and we use it to give an elementary derivation of the (previously computed) looping rate and sandpile densities of the square, triangular, and honeycomb lattices, and compute (for the first time) the looping rate and sandpile densities of many other lattices, such as the kagome lattice, the dice lattice, and the truncated hexagonal lattice (for which the values are all rational), and the square-octagon lattice Show more
Journal / seriesarXiv
Organisational unit09453 - Werner, Wendelin
NotesSubmitted 17 February 2014.
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