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Volumn 5, Issue 1, 2008, Pages 80-145

On exchangeable random variables and the statistics of large graphs and hypergraphs

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EID: 76249122786     PISSN: None     EISSN: 15495787     Source Type: Journal    
DOI: 10.1214/08-PS124     Document Type: Article
Times cited : (108)

References (69)
  • 1
    • 0001090598 scopus 로고
    • Representations for partially exchangeable arrays of random variables
    • MR0637937
    • D. J. Aldous. Representations for partially exchangeable arrays of random variables. J. Multivariate Anal., 11(4):581-598, 1981. MR0637937
    • (1981) J. Multivariate Anal. , vol.11 , Issue.4 , pp. 581-598
    • Aldous, D.J.1
  • 2
    • 0007157178 scopus 로고
    • In Ex- changeability in probability and statistics (Rome, 1981), pages 165-170. North-Holland, Amsterdam MR0675972
    • D. J. Aldous. On exchangeability and conditional independence. In Exchangeability in probability and statistics (Rome, 1981), pages 165-170. North-Holland, Amsterdam, 1982. MR0675972
    • (1982) On exchangeability and conditional independence
    • Aldous, D.J.1
  • 3
    • 0003970525 scopus 로고
    • In 'Ecole d''et'e de proba- bilit'es de Saint-Flour, XIII-1983, volume 1117 of Lecture Notes in Math., pages 1-198. Springer, Berlin, MR0883646
    • D. J. Aldous. Exchangeability and related topics. In 'Ecole d''et'e de probabilit'es de Saint-Flour, XIII-1983, volume 1117 of Lecture Notes in Math., pages 1-198. Springer, Berlin, 1985. MR0883646
    • (1985) Exchangeability and related topics
    • Aldous, D.J.1
  • 4
    • 40749096896 scopus 로고    scopus 로고
    • Processes on Unimodular Random Networks
    • MR2354165
    • D. J. Aldous and R. Lyons. Processes on Unimodular Random Networks. Electronic J. Probab., 12:1454-1508, 2007. MR2354165
    • (2007) Electronic J. Probab. , vol.12 , pp. 1454-1508
    • Aldous, D.J.1    Lyons, R.2
  • 5
    • 1842487285 scopus 로고    scopus 로고
    • The objective method: probabilistic combinatorial optimization and local weak convergence
    • In H. Kesten, editor,, pages 1-72. Springer, Berlin,MR2023650
    • D. J. Aldous and J. M. Steele. The objective method: probabilistic combinatorial optimization and local weak convergence. In H. Kesten, editor, Probability on Discrete Structures, volume 110 of Enyclopaedia Math. Sci., pages 1-72. Springer, Berlin, 2004. MR2023650
    • (2004) Probability on Discrete Structures, volume 110 of Enyclopaedia Math. Sci.
    • Aldous, D.J.1    Steele, J.M.2
  • 7
    • 84890650379 scopus 로고    scopus 로고
    • A Characterization of the (natural) Graph Properties Testable with One-Sided Error
    • preprint, available online at
    • N. Alon and A. Shapira. A Characterization of the (natural) Graph Properties Testable with One-Sided Error. preprint, available online at http://www.math.tau.ac.il/~nogaa/PDFS/heredit2.pdf.
    • Alon, N.1    Shapira, A.2
  • 8
    • 34848872557 scopus 로고    scopus 로고
    • Every monotone graph property is testable
    • In Proc. of the 37th ACM STOCBaltimore. ACM Press, . available online at, MR2181610
    • N. Alon and A. Shapira. Every monotone graph property is testable. In Proc. of the 37th ACM STOC, Baltimore. ACM Press, 2005. available online at http://www.math.tau.ac.il/~nogaa/PDFS/MonotoneSTOC.pdf. MR2181610
    • (2005)
    • Alon, N.1    Shapira, A.2
  • 12
    • 0242278812 scopus 로고    scopus 로고
    • Recurrence of distributional limits of finite planar graphs
    • MR1873300. (electronic)
    • I. Benjamini and O. Schramm. Recurrence of distributional limits of finite planar graphs. Electron. J. Probab., 6:no. 23, 13 pp. (electronic), 2001. MR1873300
    • (2001) Electron. J. Probab. , vol.6 , Issue.23 , pp. 13
    • Benjamini, I.1    Schramm, O.2
  • 15
    • 84890667440 scopus 로고    scopus 로고
    • In M. Pollicott and K. Schmidt, editors, Ergodic Theory of Zd-actions: Proceedings of the Warwick Symposium 1993-4, pages 1-61. Cambridge University Press, Cambridge, MR1411215
    • V. Bergelson. Ergodic Ramsey Theory - an Update. In M. Pollicott and K. Schmidt, editors, Ergodic Theory of Zd-actions: Proceedings of the Warwick Symposium 1993-4, pages 1-61. Cambridge University Press, Cambridge, 1996. MR1411215
    • (1996) Ergodic Ramsey Theory - an Update.
    • Bergelson, V.1
  • 18
    • 3342955888 scopus 로고
    • Fuzione caratteristica di un fenomeno aleatorio
    • B. de Finetti. Fuzione caratteristica di un fenomeno aleatorio. Mem. R. Acc. Lincei, 4(6):86-133, 1930.
    • (1930) Mem. R. Acc. Lincei , vol.4 , Issue.6 , pp. 86-133
    • de Finetti, B.1
  • 19
    • 0001918661 scopus 로고
    • La pr'evision: ses lois logiques, ses sources subjectives
    • MR1508036
    • B. de Finetti. La pr'evision: ses lois logiques, ses sources subjectives. Ann. Inst. H. Poincar'e, 7:1-68, 1937. MR1508036
    • (1937) Ann. Inst. H. Poincar'e , vol.7 , pp. 1-68
    • de Finetti, B.1
  • 20
    • 77949619619 scopus 로고    scopus 로고
    • Graph limits and exchangeable random graphs
    • Preprint; available online at arXiv.org: math.PR math.CO/0712.2749, MR2346812
    • P. Diaconis and S. Janson. Graph limits and exchangeable random graphs. Preprint; available online at arXiv.org: math.PR math.CO/0712.2749, 2007. MR2346812
    • (2007)
    • Diaconis, P.1    Janson, S.2
  • 21
    • 0002060848 scopus 로고
    • Classes of equivalent random quantities
    • MR0055601
    • E. B. Dynkin. Classes of equivalent random quantities. Uspehi Matem. Nauk (N.S.), 8(2(54)):125-130 1953. MR0055601
    • (1953) Uspehi Matem. Nauk (N.S.) , vol.8 , Issue.2-54 , pp. 125-130
    • Dynkin, E.B.1
  • 22
    • 84890772501 scopus 로고    scopus 로고
    • preprint; available online at arXiv.org: math.CO/0505335, MR2359831
    • G. Elek. On limits of finite graphs. preprint; available online at arXiv.org: math.CO/0505335, 2005. MR2359831
    • (2005) On limits of finite graphs
    • Elek, G.1
  • 25
    • 15944376146 scopus 로고
    • Some remarks on set theory, IX. Combinatorial problems in measure theory and set theory
    • MR0171713
    • P. Erdos and A. Hajnal. Some remarks on set theory, IX. Combinatorial problems in measure theory and set theory. Michigan Math. J., 11:107-127, 1964. MR0171713
    • (1964) Michigan Math. J. , vol.11 , pp. 107-127
    • Erdos, P.1    Hajnal, A.2
  • 26
    • 0346121132 scopus 로고
    • A method for constructing (3, 4)-graphs
    • 559, MR0975195
    • D. G. Fon-Der-Flaass. A method for constructing (3, 4)-graphs. Mat. Za- metki, 44(4):546-550, 559, 1988. MR0975195
    • (1988) Mat. Za- metki , vol.44 , Issue.4 , pp. 546-550
    • Fon-Der-Flaass, D.G.1
  • 27
    • 84890755245 scopus 로고    scopus 로고
    • available online at
    • D. H. Fremlin. list of problems. available online at http://www.essex.ac.uk/maths/staff/fremlin/problems.htm.
    • list of problems
    • Fremlin, D.H.1
  • 28
    • 84890679717 scopus 로고    scopus 로고
    • preprint, available online at
    • D. H. Fremlin. Random equivalence relations. preprint, available online at http://www.essex.ac.uk/maths/staff/fremlin/preprints.htm, 2006.
    • (2006) Random equivalence relations
    • Fremlin, D.H.1
  • 29
    • 67649672914 scopus 로고
    • Subgraphs of random graphs
    • MR0800252
    • D. H. Fremlin and M. Talagrand. Subgraphs of random graphs. Trans. Amer. Math. Soc., 291(2):551-582, 1985. MR0800252
    • (1985) Trans. Amer. Math. Soc. , vol.291 , Issue.2 , pp. 551-582
    • Fremlin, D.H.1    Talagrand, M.2
  • 30
    • 51649169500 scopus 로고
    • Ergodic behaviour of diagonal measures and a theorem of Szemer'edi on arithmetic progressions
    • MR0498471
    • H. Furstenberg. Ergodic behaviour of diagonal measures and a theorem of Szemer'edi on arithmetic progressions. J. d'Analyse Math., 31:204-256, 1977. MR0498471
    • (1977) J. d'Analyse Math. , vol.31 , pp. 204-256
    • Furstenberg, H.1
  • 32
    • 51249184670 scopus 로고
    • An ergodic Szemer'edi Theorem for commuting transformations
    • MR0531279
    • H. Furstenberg and Y. Katznelson. An ergodic Szemer'edi Theorem for commuting transformations. J. d'Analyse Math., 34:275-291, 1978.MR0531279
    • (1978) J. d'Analyse Math. , vol.34 , pp. 275-291
    • Furstenberg, H.1    Katznelson, Y.2
  • 33
    • 51249174873 scopus 로고
    • An ergodic Szemer'edi theorem for IPsystems and combinatorial theory
    • MR0833409
    • H. Furstenberg and Y. Katznelson. An ergodic Szemer'edi theorem for IPsystems and combinatorial theory. J. d'Analyse Math., 45:117-168, 1985. MR0833409
    • (1985) J. d'Analyse Math. , vol.45 , pp. 117-168
    • Furstenberg, H.1    Katznelson, Y.2
  • 34
    • 51249163944 scopus 로고
    • Concerning measures in first-order calculi
    • MR0175755
    • H. Gaifman. Concerning measures in first-order calculi. Israel J. Math., 2:1-18, 1964. MR0175755
    • (1964) Israel J. Math. , vol.2 , pp. 1-18
    • Gaifman, H.1
  • 35
    • 4544258332 scopus 로고    scopus 로고
    • American Mathematical Society, Providence, MR1958753
    • E. Glasner. Ergodic Theory via Joinings. American Mathematical Society, Providence, 2003. MR1958753
    • (2003) Ergodic Theory via Joinings
    • Glasner, E.1
  • 37
    • 0035618488 scopus 로고    scopus 로고
    • A new proof of Szemer'edi's theorem
    • MR1844079
    • W. T. Gowers. A new proof of Szemer'edi's theorem. Geom. Funct. Anal., 11(3):465-588, 2001. MR1844079
    • (2001) Geom. Funct. Anal. , vol.11 , Issue.3 , pp. 465-588
    • Gowers, W.T.1
  • 38
    • 29744456824 scopus 로고    scopus 로고
    • Quasirandomness, counting and regularity for 3-uniform hypergraphs
    • MR2195580
    • W. T. Gowers. Quasirandomness, counting and regularity for 3-uniform hypergraphs. Combin. Probab. Comput., 15(1-2):143-184, 2006. MR2195580
    • (2006) Combin. Probab. Comput. , vol.15 , Issue.1-2 , pp. 143-184
    • Gowers, W.T.1
  • 40
    • 84967763082 scopus 로고
    • Symmetric measures on Cartesian products
    • MR0076206
    • E. Hewitt and L. J. Savage. Symmetric measures on Cartesian products. Trans. Amer. Math. Soc., 80:470-501, 1955. MR0076206
    • (1955) Trans. Amer. Math. Soc. , vol.80 , pp. 470-501
    • Hewitt, E.1    Savage, L.J.2
  • 42
    • 0039064128 scopus 로고
    • In Exchangeability in probability and statistics (Rome, 1981), pages 281-291, Amsterdam, North-Holland. MR0675982
    • D. N. Hoover. Row-columns exchangeability and a generalized model for exchangeability. In Exchangeability in probability and statistics (Rome, 1981), pages 281-291, Amsterdam, 1982. North-Holland. MR0675982
    • (1982) Row-columns exchangeability and a generalized model for exchangeability
    • Hoover, D.N.1
  • 43
    • 23444458042 scopus 로고    scopus 로고
    • Nonconventional ergodic averages and nilmanifolds
    • MR2150389
    • B. Host and B. Kra. Nonconventional ergodic averages and nilmanifolds. Ann. Math., 161(1):397-488, 2005. MR2150389
    • (2005) Ann. Math. , vol.161 , Issue.1 , pp. 397-488
    • Host, B.1    Kra, B.2
  • 44
    • 0039893463 scopus 로고
    • Symmetries on random arrays and set-indexed processes
    • MR1182678
    • O. Kallenberg. Symmetries on random arrays and set-indexed processes. J. Theoret. Probab., 5(4):727-765, 1992. MR1182678
    • (1992) J. Theoret. Probab. , vol.5 , Issue.4 , pp. 727-765
    • Kallenberg, O.1
  • 45
    • 0004201402 scopus 로고    scopus 로고
    • Probability and its Applications (New York). Springer-Verlag, New York, second edition, MR1876169
    • O. Kallenberg. Foundations of modern probability. Probability and its Applications (New York). Springer-Verlag, New York, second edition, 2002. MR1876169
    • (2002) Foundations of modern probability
    • Kallenberg, O.1
  • 47
    • 84927129559 scopus 로고
    • The representation of partition structures
    • (2), MR0509954
    • J. F. C. Kingman. The representation of partition structures. J. London Math. Soc. (2), 18(2):374-380 1978. MR0509954
    • (1978) J. London Math. Soc. , vol.18 , Issue.2 , pp. 374-380
    • Kingman, J.F.C.1
  • 48
    • 0000681935 scopus 로고
    • Uses of exchangeability
    • MR0494344
    • J. F. C. Kingman. Uses of exchangeability. Ann. Probability, 6(2):183-197, 1978. MR0494344
    • (1978) Ann. Probability , vol.6 , Issue.2 , pp. 183-197
    • Kingman, J.F.C.1
  • 50
    • 51249182896 scopus 로고
    • A class of constructions for Tur'an's (3, 4)-problem
    • MR0685045
    • A. V. Kostochka. A class of constructions for Tur'an's (3, 4)-problem. Com- binatorica, 2:187-192, 1982. MR0685045
    • (1982) Com- binatorica , vol.2 , pp. 187-192
    • Kostochka, A.V.1
  • 51
    • 35348972404 scopus 로고
    • Representation of symmetric probability models
    • MR0275482
    • P. H. Krauss. Representation of symmetric probability models. J. Symbolic Logic, 34:183-193, 1969. MR0275482
    • (1969) J. Symbolic Logic , vol.34 , pp. 183-193
    • Krauss, P.H.1
  • 52
    • 33845276522 scopus 로고    scopus 로고
    • Limits of dense graph sequences
    • MR2274085
    • L. Lov'asz and B. Szegedy. Limits of dense graph sequences. J. Combin. Theory Ser. B, 96(6):933-957, 2006. MR2274085
    • (2006) J. Combin. Theory Ser. B , vol.96 , Issue.6 , pp. 933-957
    • Lov'asz, L.1    Szegedy, B.2
  • 54
    • 38049143735 scopus 로고    scopus 로고
    • Flag Algebras
    • MR2371204
    • A. Razborov. Flag Algebras. J. Symbolic Logic, 72(4):1239-1282, 2007. MR2371204
    • (2007) J. Symbolic Logic , vol.72 , Issue.4 , pp. 1239-1282
    • Razborov, A.1
  • 57
    • 0030128622 scopus 로고    scopus 로고
    • Robust characterization of polynomials with applications to program testing
    • MR1379300
    • R. Rubinfeld and M. Sudan. Robust characterization of polynomials with applications to program testing. SIAM Journal on Computing, 25(2):252- 271, 1996. MR1379300
    • (1996) SIAM Journal on Computing , vol.25 , Issue.2
    • Rubinfeld, R.1    Sudan, M.2
  • 58
    • 0041080490 scopus 로고
    • On stationary sequences of random variables and the de finetti's equivalence
    • MR0088823
    • C. Ryll-Nardzewski. On stationary sequences of random variables and the de finetti's equivalence. Colloq. Math., 4:149-156, 1957. MR0088823
    • (1957) Colloq. Math. , vol.4 , pp. 149-156
    • Ryll-Nardzewski, C.1
  • 59
    • 84890679539 scopus 로고    scopus 로고
    • preprint, available online at arXiv.org: math.CO/0711.3808, MR2334202
    • O. Schramm. Hyperfinite graph limits. preprint, available online at arXiv.org: math.CO/0711.3808, 2007. MR2334202
    • (2007) Hyperfinite graph limits
    • Schramm, O.1
  • 60
    • 0012824967 scopus 로고
    • What We Know and What We Do not Know about Tur'an Numbers
    • MR1341481
    • A. Sidorenko. What We Know and What We Do not Know about Tur'an Numbers. Graphs and Combinatorics, 11:179-199, 1995. MR1341481
    • (1995) Graphs and Combinatorics , vol.11 , pp. 179-199
    • Sidorenko, A.1
  • 61
    • 0001549458 scopus 로고
    • On sets of integers containing no k elements in arithmetic progression
    • MR0369312
    • E. Szemer'edi. On sets of integers containing no k elements in arithmetic progression. Acta Arith., 27:199-245, 1975. MR0369312
    • (1975) Acta Arith. , vol.27 , pp. 199-245
    • Szemer'edi, E.1
  • 62
    • 84890584608 scopus 로고    scopus 로고
    • A correspondence principle between (hyper)graph theory and probability theory, and the (hyper)graph removal lemma
    • to appear; available online at arXiv.org: math.CO/0602037. MR2373263
    • T. Tao. A correspondence principle between (hyper)graph theory and probability theory, and the (hyper)graph removal lemma. J. d'Analyse Mathematique. to appear; available online at arXiv.org: math.CO/0602037. MR2373263
    • J. d'Analyse Mathematique.
    • Tao, T.1
  • 63
    • 33750924975 scopus 로고    scopus 로고
    • A quantitative ergodic theory proof of Szemer'edi's theorem
    • Research Paper 99,(electronic), MR2274314
    • T. Tao. A quantitative ergodic theory proof of Szemer'edi's theorem. Electron. J. Combin., 13(1):Research Paper 99, 49 pp. (electronic), 2006. MR2274314
    • (2006) Electron. J. Combin. , vol.13 , Issue.1 , pp. 49
    • Tao, T.1
  • 64
    • 33845302486 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, MR2289012
    • T. Tao and V. Vu. Additive combinatorics. Cambridge University Press, Cambridge, 2006. MR2289012
    • (2006) Additive combinatorics
    • Tao, T.1    Vu, V.2
  • 66
    • 0004021335 scopus 로고
    • Classics in Mathematics. Springer-Verlag, Berlin, Reprint of the sixth (1980) edition. MR1336382
    • K. Yosida. Functional analysis. Classics in Mathematics. Springer-Verlag, Berlin, 1995. Reprint of the sixth (1980) edition. MR1336382
    • (1995) Functional analysis
    • Yosida, K.1
  • 67
    • 33750913592 scopus 로고    scopus 로고
    • Universal characteristic factors and Furstenberg averages
    • MR2257397,(electronic)
    • T. Ziegler. Universal characteristic factors and Furstenberg averages. J. Amer. Math. Soc., 20(1):53-97 (electronic), 2007. MR2257397
    • (2007) J. Amer. Math. Soc. , vol.20 , Issue.1 , pp. 53-97
    • Ziegler, T.1
  • 68
    • 84972490999 scopus 로고
    • Ergodic actions with generalized discrete spectrum
    • MR0414832
    • R. J. Zimmer. Ergodic actions with generalized discrete spectrum. Illinois J. Math., 20(4):555-588, 1976. MR0414832
    • (1976) Illinois J. Math. , vol.20 , Issue.4 , pp. 555-588
    • Zimmer, R.J.1
  • 69
    • 84972488071 scopus 로고
    • Extensions of ergodic group actions
    • MR0409770
    • R. J. Zimmer. Extensions of ergodic group actions. Illinois J. Math., 20(3):373-409, 1976. MR0409770
    • (1976) Illinois J. Math. , vol.20 , Issue.3 , pp. 373-409
    • Zimmer, R.J.1


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