Uniform infinite planar quadrangulations with a boundary

Details Uniform infinite planar quadrangulations with a boundary Uniform infinite planar quadrangulations with a boundary

2012-02-24

arxiv.org/abs/1202.5452v1

Mathematics

Probability

Scientific paper

We introduce and study the uniform infinite planar quadrangulation (UIPQ) with a boundary via an extension of the construction of arXiv:1201.1052. We then relate this object to its simple boundary analog using a pruning procedure. This enables us to study the aperture of these maps, that is, the maximal distance between two points on the boundary, which in turn sheds new light on the geometry of the UIPQ. In particular we prove that the self-avoiding walk on the UIPQ is diffusive.

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