A RECURRENCE/TRANSIENCE RESULT FOR CIRCLE PACKINGS

@inproceedings{McCAUGHAN1998ARR,
  title={A RECURRENCE/TRANSIENCE RESULT FOR CIRCLE PACKINGS},
  author={GARETH McCAUGHAN},
  year={1998}
}
  • GARETH McCAUGHAN
  • Published 1998
It is known that any infinite simplicial complex homeomorphic to the plane and satisfying a couple of other conditions is the nerve of a circle packing of either the plane or the disc (and not of both). We prove that such a complex is the nerve of a packing of the plane or the disc according as the simple random walk on its 1-skeleton is recurrent or transient, and discuss some applications. We also prove a criterion for transience of simple random walk on the 1-skeleton of a triangulation of… CONTINUE READING

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