Timár, Ádám Ends in free minimal spanning forests. (English) Zbl 1255.60173 Ann. Probab. 34, No. 3, 865-869 (2006). Summary: We show that for a transitive unimodular graphs, the number of ends is the same for every tree of the free minimal spanning forest. This answers a question of R. Lyons, Y. Peres and O. Schramm [Ann. Probab. 34, No. 5, 1665–1692 (2006; Zbl 1142.60065)]. Cited in 7 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B43 Percolation 05A05 Permutations, words, matrices 60D05 Geometric probability and stochastic geometry Keywords:minimal spanning forest; number of ends; indistinguishability Citations:Zbl 1142.60065 × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] 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. · Zbl 0948.60098 [2] Lyons, R., Peres, Y. and Schramm, O. (2006). Minimal spanning forests. Ann. Probab. 34 . · Zbl 1142.60065 · doi:10.1214/009117906000000269 [3] Lyons, L. and Schramm, O. (1999). Indistinguishability of percolation clusters. Ann. Probab. 27 1809–1836. · Zbl 0960.60013 · doi:10.1214/aop/1022677549 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.