Corpus ID: 214605633

Scaling limits of the three-dimensional uniform spanning tree and associated random walk

  title={Scaling limits of the three-dimensional uniform spanning tree and associated random walk},
  author={O. Angel and D. Croydon and S. Hernandez-Torres and Daisuke Shiraishi},
  journal={arXiv: Probability},
We show that the law of the three-dimensional uniform spanning tree (UST) is tight under rescaling in a space whose elements are measured, rooted real trees, continuously embedded into Euclidean space. We also establish that the relevant laws actually converge along a particular scaling sequence. The techniques that we use to establish these results are further applied to obtain various properties of the intrinsic metric and measure of any limiting space, including showing that the Hausdorff… Expand
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  • D. Croydon
  • Mathematics
  • Advances in Applied Probability
  • 2010
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