메뉴 건너뛰기




Volumn 25, Issue 1, 1997, Pages 30-55

Approximation of subadditive functions and convergence rates in limiting-shape results

Author keywords

Connectivity function; First passage percolation; Longest common subsequence; Oriented first passage percolation; Subadditivity

Indexed keywords


EID: 0031514908     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1024404277     Document Type: Article
Times cited : (73)

References (23)
  • 1
    • 0000629065 scopus 로고
    • Lower bounds on the connectivity function in all directions for Bernoulli percolation in two and three dimensions
    • ALEXANDER, K. S. (1990). Lower bounds on the connectivity function in all directions for Bernoulli percolation in two and three dimensions. Ann, Probab. 18 1547-1562.
    • (1990) Ann, Probab. , vol.18 , pp. 1547-1562
    • Alexander, K.S.1
  • 2
    • 0000872792 scopus 로고
    • A note on some rates of convergence in first-passage percolation
    • ALEXANDER, K. S. (1993). A note on some rates of convergence in first-passage percolation. Ann. Appl. Probab. 3 81-90.
    • (1993) Ann. Appl. Probab. , vol.3 , pp. 81-90
    • Alexander, K.S.1
  • 3
    • 0038521942 scopus 로고
    • The rate of convergence of the mean length of the longest common subsequence
    • ALEXANDER, K. S. (1994). The rate of convergence of the mean length of the longest common subsequence. Ann. Appl. Probab. 4 1074-1082.
    • (1994) Ann. Appl. Probab. , vol.4 , pp. 1074-1082
    • Alexander, K.S.1
  • 4
    • 0002005827 scopus 로고
    • The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional bernoulli percolation
    • ALEXANDER, K. S., CHAYES, J. T. and CHAYES, L. (1990). The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation. Comm. Math. Phys. 131 1-50.
    • (1990) Comm. Math. Phys. , vol.131 , pp. 1-50
    • Alexander, K.S.1    Chayes, J.T.2    Chayes, L.3
  • 5
    • 0001619220 scopus 로고
    • A phase transition for the score in matching random sequences allowing deletions
    • ARRATIA, R. and WATERMAN, M. S. (1994). A phase transition for the score in matching random sequences allowing deletions. Ann. Appl. Probab. 4 200-225.
    • (1994) Ann. Appl. Probab. , vol.4 , pp. 200-225
    • Arratia, R.1    Waterman, M.S.2
  • 6
    • 84972574511 scopus 로고
    • Weighted sums of certain dependent random variables
    • AZUMA, K. (1967). Weighted sums of certain dependent random variables. Tohuku Math. J. 19 357-367.
    • (1967) Tohuku Math. J. , vol.19 , pp. 357-367
    • Azuma, K.1
  • 7
    • 0001043080 scopus 로고
    • Statistical mechanical methods in particle structure analysis of lattice field theories. I. General results
    • BRICMONT, J. and FRÖHLICH, J. (1985a). Statistical mechanical methods in particle structure analysis of lattice field theories. I. General results. Nuclear Phys. B 251 517-552.
    • (1985) Nuclear Phys. B , vol.251 , pp. 517-552
    • Bricmont, J.1    Fröhlich, J.2
  • 8
    • 0001038009 scopus 로고
    • Statistical mechanical methods in particle structure analysis of lattice field theories. II. Scalar and surface models
    • BRICMONT, J. and FRÖHLICH, J. (1985b). Statistical mechanical methods in particle structure analysis of lattice field theories. II. Scalar and surface models. Comm. Math. Phys. 98 553-578.
    • (1985) Comm. Math. Phys. , vol.98 , pp. 553-578
    • Bricmont, J.1    Fröhlich, J.2
  • 9
    • 0000959608 scopus 로고
    • Gaussian fluctuations of connectivities in the subcritical regime of percolation
    • CAMPANINO, M., CHAYES, J. T. and CHAYES, L. (1991). Gaussian fluctuations of connectivities in the subcritical regime of percolation. Probab. Theory Related Fields 88 269-341.
    • (1991) Probab. Theory Related Fields , vol.88 , pp. 269-341
    • Campanino, M.1    Chayes, J.T.2    Chayes, L.3
  • 10
    • 0000440316 scopus 로고
    • Ornstein-Zernike behavior for self-avoiding walks at all noncritical temperatures
    • CHAYES, J. T. and CHAYES, L. (1986). Ornstein-Zernike behavior for self-avoiding walks at all noncritical temperatures. Comm. Math. Phys. 105 221-238.
    • (1986) Comm. Math. Phys. , vol.105 , pp. 221-238
    • Chayes, J.T.1    Chayes, L.2
  • 11
    • 0000151141 scopus 로고
    • Some limit theorems for percolation processes with necessary and sufficient conditions
    • COX, J. T. and DURRETT, R. (1981). Some limit theorems for percolation processes with necessary and sufficient conditions. Ann. Probab. 9 583-603.
    • (1981) Ann. Probab. , vol.9 , pp. 583-603
    • Cox, J.T.1    Durrett, R.2
  • 12
    • 84990710885 scopus 로고
    • Upper bound for the expected length of a longest common subsequence of two binary sequences
    • DANČÍK, V. and PATERSON, M. (1994). Upper bound for the expected length of a longest common subsequence of two binary sequences. Random Structures and Algorithms 6 449-458.
    • (1994) Random Structures and Algorithms , vol.6 , pp. 449-458
    • Dančík, V.1    Paterson, M.2
  • 13
    • 0010568711 scopus 로고
    • Some limit results for longest common subsequences
    • DEKEN, J. (1979). Some limit results for longest common subsequences. Discrete Math. 26 17-31.
    • (1979) Discrete Math. , vol.26 , pp. 17-31
    • Deken, J.1
  • 14
    • 0000500154 scopus 로고
    • A two-dimensional growth process
    • Univ. California Press, Berkeley
    • EDEN, M. (1961). A two-dimensional growth process. Proc. Fourth Berkeley Symp. Math. Statist. Probab. 4 223-239. Univ. California Press, Berkeley.
    • (1961) Proc. Fourth Berkeley Symp. Math. Statist. Probab. , vol.4 , pp. 223-239
    • Eden, M.1
  • 15
    • 0002446794 scopus 로고
    • A lower bound for the critical probability in a certain percolation process
    • HARRIS, T. E. (1960). A lower bound for the critical probability in a certain percolation process. Proc. Cambridge Philos. Soc. 56 13-20.
    • (1960) Proc. Cambridge Philos. Soc. , vol.56 , pp. 13-20
    • Harris, T.E.1
  • 18
    • 0000872791 scopus 로고
    • On the speed of convergence in first-passage percolation
    • KESTEN, H. (1993). On the speed of convergence in first-passage percolation. Ann. Appl. Probab. 3 296-338.
    • (1993) Ann. Appl. Probab. , vol.3 , pp. 296-338
    • Kesten, H.1
  • 19
    • 0001656464 scopus 로고
    • The ergodic theory of subadditive stochastic processes
    • KINGMAN, J. F. C. (1968). The ergodic theory of subadditive stochastic processes. J. Roy. Statist. Soc. Ser. B 30 499-510.
    • (1968) J. Roy. Statist. Soc. Ser. B , vol.30 , pp. 499-510
    • Kingman, J.F.C.1
  • 20
    • 0000354159 scopus 로고
    • Accidental deviations of density and opalescence at the critical point of a single substance
    • Academy of Sciences, Amsterdam
    • ORNSTEIN, L. S. and ZERNIKE, F. (1914). Accidental deviations of density and opalescence at the critical point of a single substance. Proceedings of the Section of Sciences (Academy of Sciences, Amsterdam) 17 793-806.
    • (1914) Proceedings of the Section of Sciences , vol.17 , pp. 793-806
    • Ornstein, L.S.1    Zernike, F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.