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Volumn 14, Issue 1, 2001, Pages 165-187

A Martingale Approach in the Study of Percolation Clusters on the Zd Lattice

Author keywords

Large deviation; Martingale; Percolation

Indexed keywords


EID: 0035645596     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007877216583     Document Type: Article
Times cited : (14)

References (11)
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    • Akcoglu, M.1    Krengel, U.2
  • 2
    • 0000145022 scopus 로고
    • Central limit theorems for associated random variables and the percolation model
    • Cox, T., and Grimmett G. (1984). Central limit theorems for associated random variables and the percolation model. Ann. Probab. 12, 514-528.
    • (1984) Ann. Probab. , vol.12 , pp. 514-528
    • Cox, T.1    Grimmett, G.2
  • 3
    • 34250106099 scopus 로고    scopus 로고
    • Large deviations for the contact process and two-dimension percolation
    • Durrett, R., and Schonmann, R. Large deviations for the contact process and two-dimension percolation. Ann. Probab. 77, 583-603.
    • Ann. Probab. , vol.77 , pp. 583-603
    • Durrett, R.1    Schonmann, R.2
  • 5
    • 0001710365 scopus 로고
    • The incipient infinite cluster in two-dimensional percolation
    • Kesten, H. (1986). The incipient infinite cluster in two-dimensional percolation. Probab. Theory Related Fields 73, 369-394.
    • (1986) Probab. Theory Related Fields , vol.73 , pp. 369-394
    • Kesten, H.1
  • 6
    • 0002023496 scopus 로고
    • The probability of a large finite cluster in super critical Bernoulli percolation
    • Kesten, H., and Zhang, Y. (1990). The probability of a large finite cluster in super critical Bernoulli percolation. Ann. Probab. 18, 537-555; Related Fields 107, 137-160 (1997).
    • (1990) Ann. Probab. , vol.18 , pp. 537-555
    • Kesten, H.1    Zhang, Y.2
  • 7
    • 0031074947 scopus 로고    scopus 로고
    • Kesten, H., and Zhang, Y. (1990). The probability of a large finite cluster in super critical Bernoulli percolation. Ann. Probab. 18, 537-555; Related Fields 107, 137-160 (1997).
    • (1997) Related Fields , vol.107 , pp. 137-160
  • 8
    • 0031074947 scopus 로고    scopus 로고
    • A central limit theorem for critical first passage percolation in two dimensions
    • Kesten, H., and Zhang, Y. (1997). A central limit theorem for critical first passage percolation in two dimensions. Probab. Theory Relat. Fields 107, 137-160.
    • (1997) Probab. Theory Relat. Fields , vol.107 , pp. 137-160
    • Kesten, H.1    Zhang, Y.2
  • 9
    • 0000964674 scopus 로고
    • Dependent central limit theorems and invariance principles
    • Mcleish, D. L. (1974). Dependent central limit theorems and invariance principles. Ann. Probab. 2, 620-628.
    • (1974) Ann. Probab. , vol.2 , pp. 620-628
    • Mcleish, D.L.1
  • 10
    • 0002318239 scopus 로고
    • Multiparameter subadditive processes
    • Smythe, R. (1976). Multiparameter subadditive processes. Ann. Probab. 4, 772-782.
    • (1976) Ann. Probab. , vol.4 , pp. 772-782
    • Smythe, R.1


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