Annals of Probability

Ends in free minimal spanning forests

Ádám Timár

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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

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

First available in Project Euclid: 27 June 2006

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Zentralblatt MATH identifier

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

Minimal spanning forest number of ends indistinguishability


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

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  • Häggstr öm, 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.