Indistinguishability of trees in uniform spanning forests

@article{Hutchcroft2015IndistinguishabilityOT,
  title={Indistinguishability of trees in uniform spanning forests},
  author={Tom Hutchcroft and Asaf Nachmias},
  journal={Probability Theory and Related Fields},
  year={2015},
  volume={168},
  pages={113-152}
}
  • Tom Hutchcroft, Asaf Nachmias
  • Published 2015
  • Mathematics, Physics
  • Probability Theory and Related Fields
  • We prove that in both the free and the wired uniform spanning forest (FUSF and WUSF) of any unimodular random rooted network (in particular, of any Cayley graph), it is impossible to distinguish the connected components of the forest from each other by invariantly defined graph properties almost surely. This confirms a conjecture of Benjamini et al. (Ann Probab 29(1):1–65, 2001). We also answer positively two additional questions of Benjamini et al. (Ann Probab 29(1):1–65, 2001) under the… CONTINUE READING

    Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

    Figures from this paper.

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 37 REFERENCES

    Choosing a Spanning Tree for the Integer Lattice Uniformly

    VIEW 8 EXCERPTS
    HIGHLY INFLUENTIAL

    Processes on unimodular random networks, Electron

    • David Aldous, Russell Lyons
    • J. Probab
    • 2007
    VIEW 11 EXCERPTS
    HIGHLY INFLUENTIAL

    Indistinguishability of Percolation Clusters

    VIEW 10 EXCERPTS
    HIGHLY INFLUENTIAL

    Generating random spanning trees more quickly than the cover time

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Anchored expansion

    • I. Benjamini, E. Paquette, J. Pfeffer
    • speed, and the hyperbolic Poisson Voronoi tessellation, ArXiv e-prints
    • 2014
    VIEW 1 EXCERPT