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Volumn 34, Issue 5, 2006, Pages 1665-1692

Minimal spanning forests

Author keywords

Amenability; Cayley graphs; Percolation; Spanning trees

Indexed keywords


EID: 33746180665     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117906000000269     Document Type: Article
Times cited : (49)

References (42)
  • 1
    • 0001347471 scopus 로고
    • Kazhdan groups, cocycles and trees
    • MR1047300
    • ADAMS, S. R. and SPATZIER, R. J. (1990). Kazhdan groups, cocycles and trees. Amer. J. Math. 112 271-287. MR1047300
    • (1990) Amer. J. Math. , vol.112 , pp. 271-287
    • Adams, S.R.1    Spatzier, R.J.2
  • 2
    • 0033415760 scopus 로고    scopus 로고
    • Scaling limits for minimal and random spanning trees in two dimensions
    • MR1716768
    • AIZENMAN, M., BURCHARD, A., NEWMAN, C. M. and WILSON, D. B. (1999). Scaling limits for minimal and random spanning trees in two dimensions. Random Structures Algorithms 15 319-367. MR1716768
    • (1999) Random Structures Algorithms , vol.15 , pp. 319-367
    • Aizenman, M.1    Burchard, A.2    Newman, C.M.3    Wilson, D.B.4
  • 3
    • 0001455013 scopus 로고
    • Asymptotics for Euclidean minimal spanning trees on random points
    • MR1161188
    • ALDOUS, D. J. and STEELE, J. M. (1992). Asymptotics for Euclidean minimal spanning trees on random points. Probab. Theory Related Fields 92 247-258. MR1161188
    • (1992) Probab. Theory Related Fields , vol.92 , pp. 247-258
    • Aldous, D.J.1    Steele, J.M.2
  • 4
    • 1842487285 scopus 로고    scopus 로고
    • The objective method: Probabilistic combinatorial optimization and local weak convergence
    • (H. Kesten, ed.). Springer, Berlin. MR2023650
    • ALDOUS, D. J. and STEELE, J. M. (2004). The objective method: Probabilistic combinatorial optimization and local weak convergence. In Probability on Discrete Structures. Encyclopaedia Math. Sci. (H. Kesten, ed.) 110 1-72. Springer, Berlin. MR2023650
    • (2004) Probability on Discrete Structures. Encyclopaedia Math. Sci. , vol.110 , pp. 1-72
    • Aldous, D.J.1    Steele, J.M.2
  • 5
    • 0002217156 scopus 로고
    • Percolation and minimal spanning forests in infinite graphs
    • MR1330762
    • ALEXANDER, K. S. (1995). Percolation and minimal spanning forests in infinite graphs. Ann. Probab. 23 87-104. MR1330762
    • (1995) Ann. Probab. , vol.23 , pp. 87-104
    • Alexander, K.S.1
  • 6
    • 21844527502 scopus 로고
    • Percolation of level sets for two-dimensional random fields with lattice symmetry
    • MR 1301459
    • ALEXANDER, K. S. and MOLCHANOV, S. A. (1994). Percolation of level sets for two-dimensional random fields with lattice symmetry. J. Statist. Phys. 77 627-643. MR 1301459
    • (1994) J. Statist. Phys. , vol.77 , pp. 627-643
    • Alexander, K.S.1    Molchanov, S.A.2
  • 7
    • 0000280765 scopus 로고
    • Percolation in half-spaces: Equality of critical densities and continuity of the percolation probability
    • MR1124831
    • BARSKY, D. J., GRIMMETT, G. R. and NEWMAN, C. M. (1991). Percolation in half-spaces: Equality of critical densities and continuity of the percolation probability. Probab. Theory Related Fields 90 111-148. MR1124831
    • (1991) Probab. Theory Related Fields , vol.90 , pp. 111-148
    • Barsky, D.J.1    Grimmett, G.R.2    Newman, C.M.3
  • 8
    • 0033164323 scopus 로고    scopus 로고
    • Critical percolation on any nonamenable group has no infinite clusters
    • MR1733151
    • BENJAMINI, I., LYONS, R., PERES, Y. and SCHRAMM, O. (1999). Critical percolation on any nonamenable group has no infinite clusters. Ann. Probab. 27 1347-1356. MR1733151
    • (1999) Ann. Probab. , vol.27 , pp. 1347-1356
    • Benjamini, I.1    Lyons, R.2    Peres, Y.3    Schramm, O.4
  • 11
    • 0001883932 scopus 로고    scopus 로고
    • d, many questions and a few answers
    • (electronic). MR1423907
    • d, many questions and a few answers. Electron. Comm. Probab. 1 71-82 (electronic). MR1423907
    • (1996) Electron. Comm. Probab. , vol.1 , pp. 71-82
    • Benjamini, I.1    Schramm, O.2
  • 12
    • 33845482754 scopus 로고    scopus 로고
    • BENJAMINI, I. and SCHRAMM, O. (1998). Personal communication
    • BENJAMINI, I. and SCHRAMM, O. (1998). Personal communication.
  • 13
    • 0035585114 scopus 로고    scopus 로고
    • Percolation in the hyperbolic plane
    • MR1815220
    • BENJAMINI, I. and SCHRAMM, O. (2001). Percolation in the hyperbolic plane. J. Amer. Math. Soc. 14 487-507. MR1815220
    • (2001) J. Amer. Math. Soc. , vol.14 , pp. 487-507
    • Benjamini, I.1    Schramm, O.2
  • 14
    • 0000393829 scopus 로고
    • Density and uniqueness in percolation
    • MR0990777
    • BURTON, R. M. and KEANE, M. (1989). Density and uniqueness in percolation. Comm. Math. Phys. 121 501-505. MR0990777
    • (1989) Comm. Math. Phys. , vol.121 , pp. 501-505
    • Burton, R.M.1    Keane, M.2
  • 15
    • 0003831025 scopus 로고
    • Mathematical Association of America, Washington, DC. Available at
    • DOYLE, P. G. and SNELL, J. L. (1984). Random Walks and Electric Networks. Mathematical Association of America, Washington, DC. Available at http://arxiv.org/abs/math/ 0001057.MR0920811
    • (1984) Random Walks and Electric Networks
    • Doyle, P.G.1    Snell, J.L.2
  • 16
  • 17
    • 33845496574 scopus 로고    scopus 로고
    • Invariant percolation and harmonic Dirichlet functions
    • To appear
    • GABORIAU, D. (2006). Invariant percolation and harmonic Dirichlet functions. GAFA. To appear.
    • (2006) GAFA.
    • Gaboriau, D.1
  • 19
    • 0001626028 scopus 로고
    • The supercritical phase of percolation is well behaved
    • MR1068308
    • GRIMMETT, G. R. and MARSTRAND, J. M. (1990). The supercritical phase of percolation is well behaved. Proc. Roy. Soc. London Ser. A 430 439-457. MR1068308
    • (1990) Proc. Roy. Soc. London Ser. A , vol.430 , pp. 439-457
    • Grimmett, G.R.1    Marstrand, J.M.2
  • 20
    • 0002225510 scopus 로고
    • Random-cluster measures and uniform spanning trees
    • MR1357655
    • HÄGGSTRÖM, O. (1995). Random-cluster measures and uniform spanning trees. Stochastic Process. Appl. 59 267-275. MR1357655
    • (1995) Stochastic Process. Appl. , vol.59 , pp. 267-275
    • Häggström, O.1
  • 21
    • 0040453578 scopus 로고    scopus 로고
    • Infinite clusters in dependent automorphism invariant percolation on trees
    • MR1457624
    • HÄGGSTRÖM, O. (1997). Infinite clusters in dependent automorphism invariant percolation on trees. Ann. Probab. 25 1423-1436. MR1457624
    • (1997) Ann. Probab. , vol.25 , pp. 1423-1436
    • Häggström, O.1
  • 22
    • 0040759189 scopus 로고    scopus 로고
    • Uniform and minimal essential spanning forests on trees
    • MR1637387
    • HÄGGSTRÖM, O. (1998). Uniform and minimal essential spanning forests on trees. Random Structures Algorithms 12 27-50. MR1637387
    • (1998) Random Structures Algorithms , vol.12 , pp. 27-50
    • Häggström, O.1
  • 23
    • 0038934720 scopus 로고    scopus 로고
    • Monotonicity of uniqueness for percolation on Cayley graphs: All infinite clusters are born simultaneously
    • MR1676835
    • HÄGGSTRÖM, O. and PERES, Y. (1999). Monotonicity of uniqueness for percolation on Cayley graphs: All infinite clusters are born simultaneously. Probab. Theory Related Fields 113 273-285. MR1676835
    • (1999) Probab. Theory Related Fields , vol.113 , pp. 273-285
    • Häggström, O.1    Peres, Y.2
  • 24
    • 0002795385 scopus 로고    scopus 로고
    • Percolation on transitive graphs as a coalescent process: Relentless merging followed by simultaneous uniqueness
    • (M. Bramson and R. Durrett, eds.). Birkhäuser, Boston. MR1703125
    • HÄGGSTRÖM, O., PERES, Y. and SCHONMANN, R. H. (1999). Percolation on transitive graphs as a coalescent process: Relentless merging followed by simultaneous uniqueness. In Perplexing Problems in Probability (M. Bramson and R. Durrett, eds.) 69-90. Birkhäuser, Boston. MR1703125
    • (1999) Perplexing Problems in Probability , pp. 69-90
    • Häggström, O.1    Peres, Y.2    Schonmann, R.H.3
  • 25
    • 0003353103 scopus 로고
    • Mean-field behaviour and the lace expansion
    • (G. Grimmett, ed.). Kluwer, Dordrecht. MR1283177
    • HARA, T. and SLADE, G. (1994). Mean-field behaviour and the lace expansion. In Probability and Phase Transition (G. Grimmett, ed.) 87-122. Kluwer, Dordrecht. MR1283177
    • (1994) Probability and Phase Transition , pp. 87-122
    • Hara, T.1    Slade, G.2
  • 26
    • 0002446794 scopus 로고
    • A lower bound for the critical probability in a certain percolation process
    • MR0115221
    • HARRIS, T. E. (1960). A lower bound for the critical probability in a certain percolation process. Proc. Cambridge Philos. Soc. 56 13-20. MR0115221
    • (1960) Proc. Cambridge Philos. Soc. , vol.56 , pp. 13-20
    • Harris, T.E.1
  • 27
    • 0002697969 scopus 로고
    • The critical probability of bond percolation on the square lattice equals 1/2
    • MR0575895
    • KESTEN, H. (1980). The critical probability of bond percolation on the square lattice equals 1/2. Comm. Math. Phys. 74 41-59. MR0575895
    • (1980) Comm. Math. Phys. , vol.74 , pp. 41-59
    • Kesten, H.1
  • 29
    • 0034345423 scopus 로고    scopus 로고
    • Phase transitions on nonamenable graphs
    • MR1757952
    • LYONS, R. (2000). Phase transitions on nonamenable graphs. J. Math. Phys. 41 1099-1126. MR1757952
    • (2000) J. Math. Phys. , vol.41 , pp. 1099-1126
    • Lyons, R.1
  • 32
    • 0033233663 scopus 로고    scopus 로고
    • Indistinguishability of percolation clusters
    • MR1742889
    • LYONS, R. and SCHRAMM, O. (1999). Indistinguishability of percolation clusters. Ann. Probab. 27 1809-1836. MR1742889
    • (1999) Ann. Probab. , vol.27 , pp. 1809-1836
    • Lyons, R.1    Schramm, O.2
  • 33
    • 0038609542 scopus 로고    scopus 로고
    • The components of the wired spanning forest are recurrent
    • MR 1961344
    • MORRIS, B. (2003). The components of the wired spanning forest are recurrent. Probab. Theory Related Fields 125 259-265. MR 1961344
    • (2003) Probab. Theory Related Fields , vol.125 , pp. 259-265
    • Morris, B.1
  • 35
    • 0001356366 scopus 로고    scopus 로고
    • Ground-state structure in a highly disordered spin-glass model
    • MR1372437
    • NEWMAN, C. M. and STEIN, D. L. (1996). Ground-state structure in a highly disordered spin-glass model. J. Statist. Phys. 82 1113-1132. MR1372437
    • (1996) J. Statist. Phys. , vol.82 , pp. 1113-1132
    • Newman, C.M.1    Stein, D.L.2
  • 36
    • 0000000702 scopus 로고
    • Choosing a spanning tree for the integer lattice uniformly
    • MR1127715
    • PEMANTLE, R. (1991). Choosing a spanning tree for the integer lattice uniformly. Ann. Probab. 191559-1574. MR1127715
    • (1991) Ann. Probab. , pp. 191559-191574
    • Pemantle, R.1
  • 37
    • 0346384827 scopus 로고    scopus 로고
    • Nonamenable products are not treeable
    • MR1776080
    • PEMANTLE, R. and PERES, Y. (2000). Nonamenable products are not treeable. Israel J. Math. 118 147-155. MR1776080
    • (2000) Israel J. Math. , vol.118 , pp. 147-155
    • Pemantle, R.1    Peres, Y.2
  • 38
    • 22044458413 scopus 로고    scopus 로고
    • The number of infinite clusters in dynamical percolation
    • MR1626782
    • PERES, Y. and STEIF, J. E. (1998). The number of infinite clusters in dynamical percolation. Probab. Theory Related Fields III 141-165. MR1626782
    • (1998) Probab. Theory Related Fields III , pp. 141-165
    • Peres, Y.1    Steif, J.E.2
  • 39
    • 0001791767 scopus 로고    scopus 로고
    • Percolation in ∞ + 1 dimensions at the uniqueness threshold
    • (M. Bramson and R. Durrett, eds.). Birkhäuser, Boston. MR 1703124
    • SCHONMANN, R. H. (1999). Percolation in ∞ + 1 dimensions at the uniqueness threshold. In Perplexing Problems in Probability (M. Bramson and R. Durrett, eds.) 53-67. Birkhäuser, Boston. MR 1703124
    • (1999) Perplexing Problems in Probability , pp. 53-67
    • Schonmann, R.H.1
  • 40
    • 0033077109 scopus 로고    scopus 로고
    • Stability of infinite clusters in supercritical percolation
    • MR1676831
    • SCHONMANN, R. H. (1999). Stability of infinite clusters in supercritical percolation. Probab. Theory Related Fields 113 287-300. MR1676831
    • (1999) Probab. Theory Related Fields , vol.113 , pp. 287-300
    • Schonmann, R.H.1
  • 41
    • 33746185705 scopus 로고    scopus 로고
    • Ends in free minimal spanning forests
    • TIMÁR, A. (2006). Ends in free minimal spanning forests. Ann. Probab. 34 865-869.
    • (2006) Ann. Probab. , vol.34 , pp. 865-869
    • Timár, A.1
  • 42
    • 0022116584 scopus 로고
    • Inequalities with applications to percolation and reliability
    • MR0799280
    • VAN DEN BERG, J. and KESTEN, H. (1985). Inequalities with applications to percolation and reliability. J. Appl. Probab. 22 556-569. MR0799280
    • (1985) J. Appl. Probab. , vol.22 , pp. 556-569
    • Van Den Berg, J.1    Kesten, H.2


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