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Volumn 51, Issue 1, 2017, Pages 52-89

Convergent sequences of sparse graphs: A large deviations approach

Author keywords

combinatorial optimization; graph convergence; sparse graphs; statistical physics

Indexed keywords


EID: 85006100222     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20694     Document Type: Article
Times cited : (7)

References (34)
  • 1
    • 84926368658 scopus 로고    scopus 로고
    • On the concentration of the number of solutions of random satisfiability formulas
    • E. Abbe and A. Montanari, On the concentration of the number of solutions of random satisfiability formulas, Random Struct Algorithms 45 (2014), 362–382.
    • (2014) Random Struct Algorithms , vol.45 , pp. 362-382
    • Abbe, E.1    Montanari, A.2
  • 2
    • 85027958359 scopus 로고    scopus 로고
    • Benjamini-Schramm convergence and the distribution of chromatic roots for sparse graphs
    • M. Abért and T. Hubai, Benjamini-Schramm convergence and the distribution of chromatic roots for sparse graphs, Combinatorica 35 (2015), 127–151.
    • (2015) Combinatorica , vol.35 , pp. 127-151
    • Abért, M.1    Hubai, T.2
  • 3
    • 40749096896 scopus 로고    scopus 로고
    • Processes on unimodular random networks
    • D. Aldous and R. Lyons, Processes on unimodular random networks, Electron J Probab 12 (2007), 1454–1508.
    • (2007) Electron J Probab , vol.12 , pp. 1454-1508
    • Aldous, D.1    Lyons, R.2
  • 4
    • 1842487285 scopus 로고    scopus 로고
    • The objective method: Probabilistic combinatorial optimization and local weak convergence
    • In, H. Kesten, editor,, Springer Berlin Heidelberg
    • D. Aldous and J. M. Steele, The objective method: Probabilistic combinatorial optimization and local weak convergence, In H. Kesten, editor, Probability on Discrete Structures, Springer Berlin Heidelberg, 2004, pp. 1–72.
    • (2004) Probability on Discrete Structures , pp. 1-72
    • Aldous, D.1    Steele, J.M.2
  • 5
    • 0242339395 scopus 로고    scopus 로고
    • Uniform infinite planar triangulations
    • O. Angel and O. Schramm, Uniform infinite planar triangulations, Commun Math Phys 241 (2003), 191–213.
    • (2003) Commun Math Phys , vol.241 , pp. 191-213
    • Angel, O.1    Schramm, O.2
  • 6
    • 84888409119 scopus 로고    scopus 로고
    • Combinatorial approach to the interpolation method and scaling limits in sparse random graphs
    • M. Bayati, D. Gamarnik, and P. Tetali, Combinatorial approach to the interpolation method and scaling limits in sparse random graphs, Ann Probab 41 (2013), 4080–4115.
    • (2013) Ann Probab , vol.41 , pp. 4080-4115
    • Bayati, M.1    Gamarnik, D.2    Tetali, P.3
  • 8
    • 0242278812 scopus 로고    scopus 로고
    • Recurrence of distributional limits of finite planar graphs
    • I. Benjamini and O. Schramm, Recurrence of distributional limits of finite planar graphs, Electron J Probab 23 (2001), 1–13.
    • (2001) Electron J Probab , vol.23 , pp. 1-13
    • Benjamini, I.1    Schramm, O.2
  • 11
    • 79959433434 scopus 로고    scopus 로고
    • Sparse graphs: Metrics and random models
    • B. Bollobás and O. Riordan, Sparse graphs: Metrics and random models, Random Struct Algorithms 39 (2011), 1–38.
    • (2011) Random Struct Algorithms , vol.39 , pp. 1-38
    • Bollobás, B.1    Riordan, O.2
  • 13
    • 77952958250 scopus 로고    scopus 로고
    • Moments of two-variable functions and the uniqueness of graph limits
    • C. Borgs, J. Chayes, and L. Lovász, Moments of two-variable functions and the uniqueness of graph limits, Geom Funct Analysis 19 (2010), 1597–1619.
    • (2010) Geom Funct Analysis , vol.19 , pp. 1597-1619
    • Borgs, C.1    Chayes, J.2    Lovász, L.3
  • 14
    • 34547701801 scopus 로고    scopus 로고
    • Counting graph homomorphisms
    • In, M. Klazar, J. Kratochvil, M. Loebl, J. Matousek, R. Thomas, P. Valtr, editors,, Springer
    • C. Borgs, J. T. Chayes, L. Lovász, V. Sos, and K. Vesztergombi, Counting graph homomorphisms, In M. Klazar, J. Kratochvil, M. Loebl, J. Matousek, R. Thomas, P. Valtr editors, Topics in discrete mathematics, Springer, 2006, pp. 315–371.
    • (2006) Topics in discrete mathematics , pp. 315-371
    • Borgs, C.1    Chayes, J.T.2    Lovász, L.3    Sos, V.4    Vesztergombi, K.5
  • 15
    • 84863483499 scopus 로고    scopus 로고
    • Convergent graph sequences II: Multiway cuts and statistical physics
    • C. Borgs, J. T. Chayes, L. Lovász, V. T. Sós, and K. Vesztergombi, Convergent graph sequences II: Multiway cuts and statistical physics, Ann Math 176 (2012), 151–219.
    • (2012) Ann Math , vol.176 , pp. 151-219
    • Borgs, C.1    Chayes, J.T.2    Lovász, L.3    Sós, V.T.4    Vesztergombi, K.5
  • 16
    • 53349180210 scopus 로고    scopus 로고
    • Convergent graph sequences I: Subgraph frequencies, metric properties, and testing
    • C. Borgs, J. T. Chayes, L. Lovász, V. T. Sós, and K. Vesztergombi, Convergent graph sequences I: Subgraph frequencies, metric properties, and testing, Adv Math 219, 1801–1851.
    • Adv Math , vol.219 , pp. 1801-1851
    • Borgs, C.1    Chayes, J.T.2    Lovász, L.3    Sós, V.T.4    Vesztergombi, K.5
  • 17
    • 79960894509 scopus 로고    scopus 로고
    • The large deviation principle for the Erdös-Rényi random graph
    • S. Chatterjee and S. R. S. Varadhan, The large deviation principle for the Erdös-Rényi random graph, Eur J Combin 32 (2011), 1000–1017.
    • (2011) Eur J Combin , vol.32 , pp. 1000-1017
    • Chatterjee, S.1    Varadhan, S.R.S.2
  • 18
    • 77949678834 scopus 로고    scopus 로고
    • Ising models on locally tree-like graphs
    • A. Dembo and A. Montanari, Ising models on locally tree-like graphs, Ann Appl Probab 20 (2010), 565–592.
    • (2010) Ann Appl Probab , vol.20 , pp. 565-592
    • Dembo, A.1    Montanari, A.2
  • 19
    • 84888394811 scopus 로고    scopus 로고
    • Factor models on locally tree-like graphs
    • A. Dembo, A. Montanari, and N. Sun, Factor models on locally tree-like graphs, Ann Probab 41 (2013), 4162–4213.
    • (2013) Ann Probab , vol.41 , pp. 4162-4213
    • Dembo, A.1    Montanari, A.2    Sun, N.3
  • 23
    • 0037236649 scopus 로고    scopus 로고
    • Replica bounds for optimization problems and diluted spin systems
    • S. Franz and M. Leone, Replica bounds for optimization problems and diluted spin systems, J Stati Phys 111 (2003), 535–564.
    • (2003) J Stati Phys , vol.111 , pp. 535-564
    • Franz, S.1    Leone, M.2
  • 26
    • 0036768858 scopus 로고    scopus 로고
    • The thermodynamic limit in mean field spin glass models
    • F. Guerra and F. L. Toninelli, The thermodynamic limit in mean field spin glass models, Commun Math Phys 230 (2002), 71–79.
    • (2002) Commun Math Phys , vol.230 , pp. 71-79
    • Guerra, F.1    Toninelli, F.L.2
  • 29
    • 33845276522 scopus 로고    scopus 로고
    • Limits of dense graph sequences
    • L. Lovász and B. Szegedy, Limits of dense graph sequences, J Combin Theory Ser B 96 (2006), 933–957.
    • (2006) J Combin Theory Ser B , vol.96 , pp. 933-957
    • Lovász, L.1    Szegedy, B.2
  • 31
    • 8744274369 scopus 로고    scopus 로고
    • Bounds for diluted mean-fields spin glass models
    • D. Panchenko and M. Talagrand, Bounds for diluted mean-fields spin glass models, Probab Theory Relat Fields 130 (2004), 312–336.
    • (2004) Probab Theory Relat Fields , vol.130 , pp. 312-336
    • Panchenko, D.1    Talagrand, M.2
  • 33
    • 0035826155 scopus 로고    scopus 로고
    • Exploring complex networks
    • S. H. Strogatz, Exploring complex networks, Nature 410 (2001), 268–276.
    • (2001) Nature , vol.410 , pp. 268-276
    • Strogatz, S.H.1
  • 34
    • 0032482432 scopus 로고    scopus 로고
    • Collective dynamics of small-world networks
    • D. Watts and S. Strogatz, Collective dynamics of small-world networks, Nature 393 (1998).
    • (1998) Nature , vol.393
    • Watts, D.1    Strogatz, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.