# 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} }

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

#### Citations

##### Publications citing this paper.

SHOWING 1-9 OF 9 CITATIONS

## Kazhdan groups have cost 1

VIEW 5 EXCERPTS

CITES BACKGROUND

## Indistinguishability of collections of trees in the uniform spanning forest

VIEW 4 EXCERPTS

CITES BACKGROUND & RESULTS

## Heavy Bernoulli-percolation clusters are indistinguishable.

VIEW 1 EXCERPT

CITES BACKGROUND

## Interlacements and the wired uniform spanning forest

VIEW 1 EXCERPT

CITES METHODS

## The component graph of the uniform spanning forest: transitions in dimensions $$9,10,11,\ldots $$9,10,11,…

VIEW 1 EXCERPT

CITES BACKGROUND

#### 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

VIEW 11 EXCERPTS

HIGHLY INFLUENTIAL

## Indistinguishability of Percolation Clusters

VIEW 10 EXCERPTS

HIGHLY INFLUENTIAL

## Geometry of the Uniform Spanning Forest: Transitions in Dimensions 4, 8, 12

VIEW 9 EXCERPTS

HIGHLY INFLUENTIAL

## Generating random spanning trees more quickly than the cover time

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Probability on Trees and Networks

VIEW 3 EXCERPTS

## Anchored expansion

VIEW 1 EXCERPT

## Minimal Configurations and Sandpile Measures

VIEW 1 EXCERPT