Uniform infinite planar quadrangulations with a boundary
نویسندگان
چکیده
We introduce and study the uniform infinite planar quadrangulation (UIPQ) with a boundary via an extension of the construction of [14]. 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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عنوان ژورنال:
- Random Struct. Algorithms
دوره 47 شماره
صفحات -
تاریخ انتشار 2015