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Geometry of uniform spanning forest components in high dimensions

• Martin T. Barlow,
Department of Mathematics, University of British Columbia , Vancouver, BC V6T 1Z2, Canada
• Antal A. Járai,
Department of Mathematical Sciences, University of Bath , Claverton Down, Bath BA2 7AY, 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 forest, loop-erased random walk
 MSC Classifications: 60D05 - Geometric probability and stochastic geometry [See also 52A22, 53C65] 05C05 - Trees 31C20 - Discrete potential theory and numerical methods

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