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Volumn 19, Issue 4, 2009, Pages 1171-1194

Mean-field conditions for percolation on finite graphs

Author keywords

Giant component; Percolation; Random graphs; Scaling window

Indexed keywords


EID: 71049154050     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-009-0032-4     Document Type: Article
Times cited : (16)

References (29)
  • 2
    • 0000099356 scopus 로고
    • Tree graph inequalities and critical behavior in percolation models
    • Aizenman M., Newman C. M.: Tree graph inequalities and critical behavior in percolation models. J. Stat. Phys. 44, 393-454 (1984).
    • (1984) J. Stat. Phys. , vol.44 , pp. 393-454
    • Aizenman, M.1    Newman, C.M.2
  • 4
    • 4544271923 scopus 로고    scopus 로고
    • Percolation on finite graphs and isoperimetric inequalities
    • Alon N., Benjamini I.: Stacey A., Percolation on finite graphs and isoperimetric inequalities. Ann. Probab. 32, 1727-1745 (2004).
    • (2004) Ann. Probab. , vol.32 , pp. 1727-1745
    • Alon, N.1    Benjamini, I.2    Stacey, A.3
  • 6
    • 84968486917 scopus 로고
    • The evolution of random graphs
    • Bollobás B.: The evolution of random graphs. Trans. Amer. Math. Soc. 286, 257-274 (1984).
    • (1984) Trans. Amer. Math. Soc. , vol.286 , pp. 257-274
    • Bollobás, B.1
  • 7
    • 26944446964 scopus 로고    scopus 로고
    • Random subgraphs of finite graphs: I. The Scaling Window under the Triangle Condition
    • Borgs C., Chayes J. T., van der Hofstad R., Slade G., Spencer J.: Random subgraphs of finite graphs: I. The scaling window under the triangle condition. Rand. Struc. Alg. 27, 137-184 (2005).
    • (2005) Rand. Struc. Alg. , vol.27 , pp. 137-184
    • Borgs, C.1    Chayes, J.T.2    van der Hofstad, R.3    Slade, G.4    Spencer, J.5
  • 8
    • 27644597417 scopus 로고    scopus 로고
    • Random subgraphs of finite graphs: II. The lace expansion and the triangle condition
    • Borgs C., Chayes J. T., van der Hofstad R., Slade G., Spencer J.: Random subgraphs of finite graphs: II. The lace expansion and the triangle condition. Annals of Probability 33, 1886-1944 (2005).
    • (2005) Annals of Probability , vol.33 , pp. 1886-1944
    • Borgs, C.1    Chayes, J.T.2    van der Hofstad, R.3    Slade, G.4    Spencer, J.5
  • 9
    • 33749317177 scopus 로고    scopus 로고
    • Random subgraphs of finite graphs: III. The phase transition for the n-cube
    • Borgs C., Chayes J. T., van der Hofstad R., Slade G., Spencer J.: Random subgraphs of finite graphs: III. The phase transition for the n-cube. Combinatorica 26, 395-410 (2006).
    • (2006) Combinatorica , vol.26 , pp. 395-410
    • Borgs, C.1    Chayes, J.T.2    van der Hofstad, R.3    Slade, G.4    Spencer, J.5
  • 13
    • 0002590276 scopus 로고
    • Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process
    • Fill J. A.: Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process. Ann. Appl. Probab. 1(1), 62-87 (1991).
    • (1991) Ann. Appl. Probab. , vol.1 , Issue.1 , pp. 62-87
    • Fill, J.A.1
  • 14
    • 34249952953 scopus 로고
    • Mean-field critical behaviour for percolation in high dimensions
    • Hara T., Slade G.: Mean-field critical behaviour for percolation in high dimensions. Comm. Math. Phys. 128, 333-391 (1990).
    • (1990) Comm. Math. Phys. , vol.128 , pp. 333-391
    • Hara, T.1    Slade, G.2
  • 15
    • 71049153768 scopus 로고    scopus 로고
    • R. van der Hofstad, M. Luczak, Random subgraphs of the 2D Hamming graph: the supercritical phase, Probability Theory and Related Fields, to appear.
  • 17
    • 84990713780 scopus 로고
    • The transitive closure of a random digraph
    • Karp R. M.: The transitive closure of a random digraph. Random Structures Algorithms 1, 73-93 (1990).
    • (1990) Random Structures Algorithms , vol.1 , pp. 73-93
    • Karp, R.M.1
  • 18
    • 71049178737 scopus 로고    scopus 로고
    • G. Kozma, A. Nachmias, An upper bound for percolation on graphs with low girth, in preparation (2007).
  • 19
    • 0011514730 scopus 로고
    • Explicit construction of graphs with an arbitrary large girth and of large size
    • Lazebnik F., Ustimenko V. A.: Explicit construction of graphs with an arbitrary large girth and of large size. Discrete Appl. Math. 60(1-3), 275-284 (1995).
    • (1995) Discrete Appl. Math. , vol.60 , Issue.1-3 , pp. 275-284
    • Lazebnik, F.1    Ustimenko, V.A.2
  • 21
    • 84990709764 scopus 로고
    • Component behavior near the critical point of the random graph process
    • Łuczak T.: Component behavior near the critical point of the random graph process. Random Structures Algorithms 1, 287-310 (1990).
    • (1990) Random Structures Algorithms , vol.1 , pp. 287-310
    • Łuczak, T.1
  • 22
    • 0000862093 scopus 로고
    • Random walks, capacity and percolation on trees
    • Lyons R.: Random walks, capacity and percolation on trees. Ann. Probab. 20, 2043-2088 (1992).
    • (1992) Ann. Probab. , vol.20 , pp. 2043-2088
    • Lyons, R.1
  • 23
    • 51249182252 scopus 로고
    • Explicit constructions of graphs without short cycles and low density codes
    • Margulis G. A.: Explicit constructions of graphs without short cycles and low density codes. Combinatorica 2(1), 71-78 (1982).
    • (1982) Combinatorica , vol.2 , Issue.1 , pp. 71-78
    • Margulis, G.A.1
  • 24
    • 0000618154 scopus 로고
    • Symmetric sampling procedures, general epidemic processes and their threshold limit theorems
    • Martin-Löf A.: Symmetric sampling procedures, general epidemic processes and their threshold limit theorems. J. Appl. Probab. 23, 265-282 (1986).
    • (1986) J. Appl. Probab. , vol.23 , pp. 265-282
    • Martin-löf, A.1
  • 25
    • 0024772324 scopus 로고    scopus 로고
    • M. Mihail, Conductance and convergence of Markov chains - A combinatorial treatment of expander, Proceedings of the 30th Annual Conference on Foundations of Computer Science (FOCS 89) (1989), 526-531.
  • 27
    • 52049107366 scopus 로고    scopus 로고
    • Critical random graphs: Diameter and mixing time
    • Nachmias A., Peres Y.: Critical random graphs: diameter and mixing time. Annals of Probability 36(4), 1267-1286 (2008).
    • (2008) Annals of Probability , vol.36 , Issue.4 , pp. 1267-1286
    • Nachmias, A.1    Peres, Y.2
  • 28
    • 0000498664 scopus 로고    scopus 로고
    • Probability on trees: An introductory climb, Ecole d'été de Probabilités de Saint-Flour XXVII
    • Peres Y.: Probability on trees: an introductory climb, Ecole d'été de Probabilités de Saint-Flour XXVII. Springer Lect. Notes Math. 1717, 193-280 (1999).
    • (1999) Springer Lect. Notes Math. , vol.1717 , pp. 193-280
    • Peres, Y.1
  • 29
    • 52049109174 scopus 로고    scopus 로고
    • Edge percolation on a random regular graph of low degree
    • Pittel B.: Edge percolation on a random regular graph of low degree. Annals of Probability 36(4), 1359-1389 (2008).
    • (2008) Annals of Probability , vol.36 , Issue.4 , pp. 1359-1389
    • Pittel, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.