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Volumn 6, Issue 1, 1996, Pages 297-319

Large deviations for combinatorial distributions. I: Central limit theorems

Author keywords

Additive arithmetical functions; Central limit theorems; Combinatorial constructions; Large deviations

Indexed keywords


EID: 0030538348     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034968075     Document Type: Article
Times cited : (52)

References (40)
  • 1
    • 0015896876 scopus 로고
    • Central and local limit theorems applied to asymptotic enumeration
    • BENDER, E. A. (1973). Central and local limit theorems applied to asymptotic enumeration. J. Combin. Theory Ser. A 15 91-111.
    • (1973) J. Combin. Theory Ser. A , vol.15 , pp. 91-111
    • Bender, E.A.1
  • 4
    • 0001201781 scopus 로고
    • Central and local limit theorems for the coefficients of polynomials of binomial type
    • CANFIELD, E. R. (1977). Central and local limit theorems for the coefficients of polynomials of binomial type. J. Combin. Theory Ser. A 23 275-290.
    • (1977) J. Combin. Theory Ser. A , vol.23 , pp. 275-290
    • Canfield, E.R.1
  • 5
    • 0002226749 scopus 로고
    • Application of the Berry-Esseen inequality to combinatorial estimates
    • CANFIELD, E. R. (1980). Application of the Berry-Esseen inequality to combinatorial estimates. J. Combin. Theory Ser. A 28 17-25.
    • (1980) J. Combin. Theory Ser. A , vol.28 , pp. 17-25
    • Canfield, E.R.1
  • 6
    • 0000182415 scopus 로고
    • A measure of asymptotic efficiency for tests of a hypothesis based on the sums of observations
    • CHERNOFF, H. (1952). A measure of asymptotic efficiency for tests of a hypothesis based on the sums of observations. Ann. Math. Statist., 23 493-507.
    • (1952) Ann. Math. Statist. , vol.23 , pp. 493-507
    • Chernoff, H.1
  • 7
    • 0002178770 scopus 로고
    • Sur un nouveau théorème-limite de la théorie des probabilités
    • Herman, Paris
    • CRAMÉR, H. (1938). Sur un nouveau théorème-limite de la théorie des probabilités. In Actualités Scientifiques et Industrielles 736 5-23. Herman, Paris.
    • (1938) Actualités Scientifiques et Industrielles , vol.736 , pp. 5-23
    • Cramér, H.1
  • 8
    • 0001366699 scopus 로고
    • Sur des formules de atle selberg
    • DELANGE, H. (1971). Sur des formules de Atle Selberg. Acta Arith. 19 105-146.
    • (1971) Acta Arith. , vol.19 , pp. 105-146
    • Delange, H.1
  • 9
    • 34250598875 scopus 로고
    • Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law
    • ESSEEN, C.-G. (1945). Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law. Acta Math. 77 1-125.
    • (1945) Acta Math. , vol.77 , pp. 1-125
    • Esseen, C.-G.1
  • 11
    • 0000967099 scopus 로고
    • Sequence of operations analysis for dynamic data structures
    • FLAJOLET, P., FRANÇON, J. and VUILLEMIN, J. (1980). Sequence of operations analysis for dynamic data structures. J. Algorithms 1 111-141.
    • (1980) J. Algorithms , vol.1 , pp. 111-141
    • Flajolet, P.1    Françon, J.2    Vuillemin, J.3
  • 12
    • 0000640693 scopus 로고
    • Singularity analysis of generating functions
    • FLAJOLET, P. and ODLYZKO, A. M. (1990). Singularity analysis of generating functions. SIAM J. Discrete Math. 3 216-240.
    • (1990) SIAM J. Discrete Math. , vol.3 , pp. 216-240
    • Flajolet, P.1    Odlyzko, A.M.2
  • 13
    • 38249033735 scopus 로고
    • Level number sequences for trees
    • FLAJOLET, P. and PRODINGER, H. (1986). Level number sequences for trees. Discrete Math. 65 149-156.
    • (1986) Discrete Math. , vol.65 , pp. 149-156
    • Flajolet, P.1    Prodinger, H.2
  • 15
    • 38249019619 scopus 로고
    • Gaussian limiting distributions for the number of components in combinatorial structures
    • FLAJOLET, P. and SORIA, M. (1990). Gaussian limiting distributions for the number of components in combinatorial structures. J. Combin. Theory Ser. A 53 165-182.
    • (1990) J. Combin. Theory Ser. A , vol.53 , pp. 165-182
    • Flajolet, P.1    Soria, M.2
  • 16
    • 0000202919 scopus 로고
    • General combinatorial schemes, Gaussian limit distributions and exponential tails
    • FLAJOLET, P. and SORIA, M. (1993). General combinatorial schemes, Gaussian limit distributions and exponential tails. Discrete Math. 114 159-180.
    • (1993) Discrete Math. , vol.114 , pp. 159-180
    • Flajolet, P.1    Soria, M.2
  • 17
    • 38049026666 scopus 로고
    • Central and local limit theorems applied to asymptotic enumeration. IV. Multivariate generating functions
    • GAO, Z. and RICHMOND, L. B. (1992). Central and local limit theorems applied to asymptotic enumeration. IV. Multivariate generating functions. J. Comput. Appl. Math. 41 177-186.
    • (1992) J. Comput. Appl. Math. , vol.41 , pp. 177-186
    • Gao, Z.1    Richmond, L.B.2
  • 22
    • 0040056909 scopus 로고    scopus 로고
    • Über einen neuen grennzwertsatz der wahrscheinlichkeitsrechnung
    • KHINTCHINE, A. Über einen neuen Grennzwertsatz der Wahrscheinlichkeitsrechnung. Math. Ann. 101 745-752.
    • Math. Ann. , vol.101 , pp. 745-752
    • Khintchine, A.1
  • 23
    • 0000132946 scopus 로고
    • "Factorisatio numerorum" in arithmetical semigroups
    • KNOPFMACHER, A., KNOPFMACHER, J. and WARLIMONT, R. (1992). "Factorisatio numerorum" in arithmetical semigroups. Acta Arith. 61 327-336.
    • (1992) Acta Arith. , vol.61 , pp. 327-336
    • Knopfmacher, A.1    Knopfmacher, J.2    Warlimont, R.3
  • 28
    • 0001152945 scopus 로고
    • Probabilistic proofs of asymptotic formulas for some orthogonal polynomials
    • MAEJIMA, M. and VAN ASSCHE, W. (1985). Probabilistic proofs of asymptotic formulas for some orthogonal polynomials. Math. Proc. Cambridge Philos. Soc. 97 499-510.
    • (1985) Math. Proc. Cambridge Philos. Soc. , vol.97 , pp. 499-510
    • Maejima, M.1    Van Assche, W.2
  • 30
    • 0001270611 scopus 로고
    • On the altitude of nodes in random trees
    • MEIR, A. and MOON, J. W. (1978). On the altitude of nodes in random trees. Canad. J. Math. 30 997-1015.
    • (1978) Canad. J. Math. , vol.30 , pp. 997-1015
    • Meir, A.1    Moon, J.W.2
  • 32
    • 0040056875 scopus 로고
    • Explicit Tauberian estimates for functions with positive coefficients
    • ODLYZKU, A. M. (1992). Explicit Tauberian estimates for functions with positive coefficients. J. Comput. Appl. Math. 41 187-197.
    • (1992) J. Comput. Appl. Math. , vol.41 , pp. 187-197
    • Odlyzku, A.M.1
  • 33
    • 0004035778 scopus 로고
    • Springer, Berlin. (Translated from the Russian by A. A. Brown.)
    • PETROV, V. V. (1975). Sums of Independent Random Variables. Springer, Berlin. (Translated from the Russian by A. A. Brown.)
    • (1975) Sums of Independent Random Variables
    • Petrov, V.V.1
  • 34
    • 0038872332 scopus 로고
    • A more precise form of an inequality of S. N. Bernšteǐn. For large deviations
    • RICHTER, W. (1964). A more precise form of an inequality of S. N. Bernšteǐn. For large deviations. Selected Translations of Mathematical Statistics and Probability 4 225-232. [Originally published in Vestnik Leningrad. Univ. Mat. Mek. Astronom. 14 24-29 (1959).]
    • (1964) Selected Translations of Mathematical Statistics and Probability , vol.4 , pp. 225-232
    • Richter, W.1
  • 35
    • 0040056881 scopus 로고
    • Originally published
    • RICHTER, W. (1964). A more precise form of an inequality of S. N. Bernšteǐn. For large deviations. Selected Translations of Mathematical Statistics and Probability 4 225-232. [Originally published in Vestnik Leningrad. Univ. Mat. Mek. Astronom. 14 24-29 (1959).]
    • (1959) Vestnik Leningrad. Univ. Mat. Mek. Astronom. , vol.14 , pp. 24-29


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.