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Geometry of Uniform Spanning Forest Components in High Dimensions

Part of: Other generalizations Graph theory Geometric probability and stochastic geometry

Published online by Cambridge University Press:  07 January 2019

Martin T. Barlow  and
Antal A. Járai
Martin T. Barlow
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada Email: barlow@math.ubc.ca
Antal A. Járai
Affiliation:
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK Email: a.jarai@bath.ac.uk
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Abstract

We study the geometry of the component of the origin in the uniform spanning forest of $\mathbb{Z}^{d}$ and give bounds on the size of balls in the intrinsic metric.

Keywords

uniform spanning forestloop-erased random walk

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 05C05: Trees 31C20: Discrete potential theory and numerical methods
Type
Article
Information
Canadian Journal of Mathematics , Volume 71 , Issue 6 , December 2019 , pp. 1297 - 1321
Copyright
© Canadian Mathematical Society 2018 

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Footnotes

Research partially supported by NSERC (Canada).

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