메뉴 건너뛰기




Volumn 21, Issue 1-2, 2012, Pages 265-299

The phase transition in the configuration model

Author keywords

[No Author keywords available]

Indexed keywords

CONFIGURATION MODEL; DEGREE SEQUENCE; NATURAL EXTENSION; PERCOLATION PHASE TRANSITION; RANDOM GRAPHS; SUBGRAPHS;

EID: 84859320352     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S0963548311000666     Document Type: Article
Times cited : (77)

References (28)
  • 1
    • 0031483018 scopus 로고    scopus 로고
    • Brownian excursions, critical random graphs and the multiplicative coalescent
    • Aldous, D. (1997) Brownian excursions, critical random graphs and the multiplicative coalescent. Ann. Probab. 25 812-854.
    • (1997) Ann. Probab. , vol.25 , pp. 812-854
    • Aldous, D.1
  • 2
    • 0000664045 scopus 로고
    • The asymptotic number of labeled graphs with given degree sequences
    • Bender, E. A. and Canfield, R. E. (1978) The asymptotic number of labeled graphs with given degree sequences. J. Combin. Theory Ser. A 24 296-307.
    • (1978) J. Combin. Theory Ser. A , vol.24 , pp. 296-307
    • Bender, E.A.1    Canfield, R.E.2
  • 3
    • 85012603843 scopus 로고
    • A probabilistic proof of an asymptotic formula for the number of labelled regular graphs
    • Bollobás, B. (1980) A probabilistic proof of an asymptotic formula for the number of labelled regular graphs. European J. Combin. 1 311-316.
    • (1980) European J. Combin. , vol.1 , pp. 311-316
    • Bollobás, B.1
  • 4
    • 84968486917 scopus 로고
    • The evolution of random graphs
    • Bollobás, B. (1984) The evolution of random graphs. Trans. Amer. Math. Soc. 286 257-274.
    • (1984) Trans. Amer. Math. Soc. , vol.286 , pp. 257-274
    • Bollobás, B.1
  • 5
    • 79952711735 scopus 로고    scopus 로고
    • Random graphs and branching processes
    • (B. Bollobá s, R. Kozma and D. Miklós eds), Bolyai Soc. Math. Studies
    • Bollobás, B. and Riordan, O. (2009) Random graphs and branching processes. In Handbook of Large-Scale Random Networks (B. Bollobá s, R. Kozma and D. Miklós eds), Vol. 18 of Bolyai Soc. Math. Studies, pp. 15-115.
    • (2009) Handbook of Large-Scale Random Networks , vol.18 , pp. 15-115
    • Bollobás, B.1    Riordan, O.2
  • 6
    • 81455141562 scopus 로고    scopus 로고
    • Asymptotic normality of the size of the giant component via a random walk
    • Bollobás, B. and Riordan, O. (2012) Asymptotic normality of the size of the giant component via a random walk. J. Combin. Theory Ser. B 102 53-61.
    • (2012) J. Combin. Theory Ser. B , vol.102 , pp. 53-61
    • Bollobás, B.1    Riordan, O.2
  • 7
    • 0000047875 scopus 로고
    • Martingale central limit theorems
    • Brown, B. M. (1971) Martingale central limit theorems. Ann. Math. Statist. 42 59-66.
    • (1971) Ann. Math. Statist. , vol.42 , pp. 59-66
    • Brown, B.M.1
  • 8
    • 0002178770 scopus 로고
    • Sur un nouveau théorème-limite de la théorie des probabilités
    • Cramér, H. (1938) Sur un nouveau théorème-limite de la théorie des probabilités. Actualités Scientifiques et Industrielles 736 5-23.
    • (1938) Actualités Scientifiques et Industrielles , vol.736 , pp. 5-23
    • Cramér, H.1
  • 9
    • 78650479901 scopus 로고    scopus 로고
    • Diameters in supercritical random graphs via first-passage percolation
    • Ding, J., Kim, J. H., Lubetzky, E. and Peres, Y. (2010) Diameters in supercritical random graphs via first-passage percolation. Combin. Probab. Comput. 19 729-751.
    • (2010) Combin. Probab. Comput. , vol.19 , pp. 729-751
    • Ding, J.1    Kim, J.H.2    Lubetzky, E.3    Peres, Y.4
  • 11
    • 74349118070 scopus 로고    scopus 로고
    • Percolation on sparse random graphs with given degree sequence
    • Fountoulakis, N. (2007) Percolation on sparse random graphs with given degree sequence. Internet Mathematics 4 329-356.
    • (2007) Internet Mathematics , vol.4 , pp. 329-356
    • Fountoulakis, N.1
  • 12
    • 0034918353 scopus 로고    scopus 로고
    • The giant component threshold for random regular graphs with edge faults
    • DOI 10.1016/S0304-3975(00)00015-3, PII S0304397500000153
    • Goerdt, A. (2001) The giant component threshold for random regular graphs with edge faults. Theoret. Comput. Sci. 259 307-321. (Pubitemid 32674031)
    • (2001) Theoretical Computer Science , vol.259 , Issue.1-2 , pp. 307-321
    • Goerdt, A.1
  • 13
    • 62649110761 scopus 로고    scopus 로고
    • On percolation in random graphs with given vertex degrees
    • Janson, S. (2009) On percolation in random graphs with given vertex degrees. Electron. J. Probab. 14 87-118.
    • (2009) Electron. J. Probab. , vol.14 , pp. 87-118
    • Janson, S.1
  • 14
    • 62449296666 scopus 로고    scopus 로고
    • A new approach to the giant component problem
    • Janson, S. and Luczak, M. J. (2009) A new approach to the giant component problem. Random Struct. Alg. 34 197-216.
    • (2009) Random Struct. Alg. , vol.34 , pp. 197-216
    • Janson, S.1    Luczak, M.J.2
  • 15
    • 37249062554 scopus 로고    scopus 로고
    • The critical phase for random graphs with a given degree sequence
    • DOI 10.1017/S096354830700867X
    • Kang, M. and Seierstad, T. G. (2008) The critical phase for random graphs with a given degree sequence. Combin. Probab. Comput. 17 67-86. (Pubitemid 350273128)
    • (2008) Combinatorics Probability and Computing , vol.17 , Issue.1 , pp. 67-86
    • Kang, M.1    Seierstad, T.G.2
  • 16
    • 84990713780 scopus 로고
    • The transitive closure of a random digraph
    • Karp, R. M. (1990) The transitive closure of a random digraph. Random Struct. Alg. 1 73-93.
    • (1990) Random Struct. Alg. , vol.1 , pp. 73-93
    • Karp, R.M.1
  • 17
    • 84990709764 scopus 로고
    • Component behavior near the critical point of the random graph process
    • Luczak, T. (1990) Component behavior near the critical point of the random graph process. Random Struct. Alg. 1 287-310.
    • (1990) Random Struct. Alg. , vol.1 , pp. 287-310
    • Luczak, T.1
  • 18
    • 0000618154 scopus 로고
    • Symmetric sampling procedures, general epidemic processes and their threshold limit theorems
    • Martin-Löf, A. (1986) Symmetric sampling procedures, general epidemic processes and their threshold limit theorems. J. Appl. Probab. 23 265-282.
    • (1986) J. Appl. Probab. , vol.23 , pp. 265-282
    • Martin-Löf, A.1
  • 19
    • 0011317150 scopus 로고
    • On local limit theorem for integer valued random variables
    • McDonald, D. R. (1979) On local limit theorem for integer valued random variables. Teor. Veroyatnost. i Primenen. 24 607-614.
    • (1979) Teor. Veroyatnost. i Primenen , vol.24 , pp. 607-614
    • McDonald, D.R.1
  • 20
    • 0011317150 scopus 로고
    • See also Theory Probab. Appl. 24 (1980), 613-619.
    • (1980) Theory Probab. Appl. , vol.24 , pp. 613-619
  • 21
    • 84990671447 scopus 로고
    • A critical point for random graphs with a given degree sequence
    • Molloy, M. and Reed, B. (1995) A critical point for random graphs with a given degree sequence, Random Struct. Alg. 6 161-179.
    • (1995) Random Struct. Alg. , vol.6 , pp. 161-179
    • Molloy, M.1    Reed, B.2
  • 22
    • 0032286776 scopus 로고    scopus 로고
    • The Size of the Giant Component of a Random Graph with a Given Degree Sequence
    • Molloy, M. and Reed, B. (1998) The size of the giant component of a random graph with a given degree sequence. Combin. Probab. Comput. 7 295-305. (Pubitemid 128480814)
    • (1998) Combinatorics Probability and Computing , vol.7 , Issue.3 , pp. 295-305
    • Molloy, M.1    Reed, B.2
  • 23
    • 74349088261 scopus 로고    scopus 로고
    • Component sizes of the random graph outside the scaling window
    • Nachmias, A. and Peres, Y. (2007) Component sizes of the random graph outside the scaling window. ALEA Lat. Amer. J. Probab. Math. Stat. 3 133-142.
    • (2007) ALEA Lat. Amer. J. Probab. Math. Stat. , vol.3 , pp. 133-142
    • Nachmias, A.1    Peres, Y.2
  • 24
    • 74349101469 scopus 로고    scopus 로고
    • Critical percolation on random regular graphs
    • Nachmias, A. and Peres, Y. (2010) Critical percolation on random regular graphs. Random Struct. Alg. 36 111-148.
    • (2010) Random Struct. Alg. , vol.36 , pp. 111-148
    • Nachmias, A.1    Peres, Y.2
  • 25
    • 0004035778 scopus 로고
    • translated from the Russian by A. A. Brown, Vol. 82 of Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer
    • Petrov, V. V. (1975) Sums of Independent Random Variables, translated from the Russian by A. A. Brown, Vol. 82 of Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer.
    • (1975) Sums of Independent Random Variables
    • Petrov, V.V.1
  • 26
    • 52049109174 scopus 로고    scopus 로고
    • Edge percolation on a random regular graph of low degree
    • Pittel, B. (2008) Edge percolation on a random regular graph of low degree. Ann. Probab. 36 1359-1389.
    • (2008) Ann. Probab. , vol.36 , pp. 1359-1389
    • Pittel, B.1
  • 27
    • 12944257224 scopus 로고    scopus 로고
    • Counting connected graphs inside-out
    • DOI 10.1016/j.jctb.2004.09.005, PII S0095895604000887
    • Pittel, B. and Wormald, C. (2005) Counting connected graphs inside-out. J. Combin. Theory Ser. B 93 127-172. (Pubitemid 40176102)
    • (2005) Journal of Combinatorial Theory. Series B , vol.93 , Issue.2 , pp. 127-172
    • Pittel, B.1    Wormald, N.C.2
  • 28
    • 84967710276 scopus 로고
    • A combinatorial lemma and its application to probability theory
    • Spitzer, F. (1956) A combinatorial lemma and its application to probability theory. Trans. Amer. Math. Soc. 82 323-339.
    • (1956) Trans. Amer. Math. Soc. , vol.82 , pp. 323-339
    • Spitzer, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.