The Annals of Probability

Ends in free minimal spanning forests

Ádám Timár

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Abstract

We show that for a transitive unimodular graph, the number of ends is the same for every tree of the free minimal spanning forest. This answers a question of Lyons, Peres and Schramm.

Article information

Source
Ann. Probab., Volume 34, Number 3 (2006), 865-869.

Dates
First available in Project Euclid: 27 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.aop/1151418485

Digital Object Identifier
doi:10.1214/009117906000000025

Mathematical Reviews number (MathSciNet)
MR2243871

Zentralblatt MATH identifier
1255.60173

Subjects
Primary: 60B99: None of the above, but in this section
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Keywords
Minimal spanning forest number of ends indistinguishability

Citation

Timár, Ádám. Ends in free minimal spanning forests. Ann. Probab. 34 (2006), no. 3, 865--869. doi:10.1214/009117906000000025. https://projecteuclid.org/euclid.aop/1151418485


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References

  • Häggström, O., Peres, Y. and Schonmann, R. (1999). Percolation on transitive graphs as a coalescent process: Relentless merging followed by simultaneous uniqueness. In Perplexing Probability Problems: Papers in Honor of H. Kesten (M. Bramson and R. Durrett, eds.) 69--90. Birkhäuser, Boston.
  • Lyons, R., Peres, Y. and Schramm, O. (2006). Minimal spanning forests. Ann. Probab. 34. To appear.
  • Lyons, L. and Schramm, O. (1999). Indistinguishability of percolation clusters. Ann. Probab. 27 1809--1836.