Induced graphs of uniform spanning forests

  title={Induced graphs of uniform spanning forests},
  author={Russell Lyons and Yuval Peres and Xin Sun},
  journal={Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques},
  • R. Lyons, Y. Peres, Xin Sun
  • Published 7 December 2018
  • Mathematics
  • Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
Given a subgraph $H$ of a graph $G$, the induced graph of $H$ is the largest subgraph of $G$ whose vertex set is the same as that of $H$. Our paper concerns the induced graphs of the components of $\operatorname{WSF}(G)$, the wired spanning forest on $G$, and, to a lesser extent, $\operatorname{FSF}(G)$, the free uniform spanning forest. We show that the induced graph of each component of $\operatorname{WSF}(\mathbb Z^d$) is almost surely recurrent when $d\ge 8$. Moreover, the effective… 
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