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Volumn 31, Issue 2, 2003, Pages 1028-1051

Nondifferentiability of the time constants of first-passage percolation

Author keywords

Bernoulli percolation; Differentiability; First passage percolation; Hammersley; Longest path; Shortest path; Surgery; Time constants; Welsh

Indexed keywords


EID: 0038336102     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1048516544     Document Type: Article
Times cited : (9)

References (13)
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  • 2
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  • 3
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    • Cambridge Univ. Press
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    • (1997) Sperner Theory
    • Engle, E.1
  • 4
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    • First-passage percolation, network flows, and electrical resistances
    • GRIMMETT, G. and KESTEN, H. (1984). First-passage percolation, network flows, and electrical resistances. Z. Wahrsch. Verw. Gebiete 66 335-366.
    • (1984) Z. Wahrsch. Verw. Gebiete , vol.66 , pp. 335-366
    • Grimmett, G.1    Kesten, H.2
  • 5
    • 0002049581 scopus 로고
    • First-passage percolation, subadditive processes, stochastic networks, and generalized renewal theory
    • J. Neyman and L. Le Cam, eds. Springer, Berlin
    • HAMMERSLEY, J. M. and WELSH, D. J. A. (1965). First-passage percolation, subadditive processes, stochastic networks, and generalized renewal theory. In Bernoulli, Bayse, Laplace Anniversary Volume (J. Neyman and L. Le Cam, eds.) 61-110. Springer, Berlin.
    • (1965) Bernoulli, Bayse, Laplace Anniversary Volume , pp. 61-110
    • Hammersley, J.M.1    Welsh, D.J.A.2
  • 6
    • 84947403595 scopus 로고
    • Probability inqualities for sums of bounded random variables
    • HOEFFING, W. (1963). Probability inqualities for sums of bounded random variables. J. Amer. Statist. Assoc. 26 13-30.
    • (1963) J. Amer. Statist. Assoc. , vol.26 , pp. 13-30
    • Hoeffing, W.1
  • 7
    • 0037757168 scopus 로고
    • On the time constant and path length of first-passage percolation
    • KESTEN, H. (1980). On the time constant and path length of first-passage percolation. Adv. in Appl. Probab. 12 848-863.
    • (1980) Adv. in Appl. Probab. , vol.12 , pp. 848-863
    • Kesten, H.1
  • 9
    • 0000264803 scopus 로고
    • Aspects of first passage percolation
    • Springer, New York
    • KESTEN, H. (1986). Aspects of First Passage Percolation. Lecture Notes in Math. 1180. Springer, New York.
    • (1986) Lecture Notes in Math. , vol.1180
    • Kesten, H.1
  • 10
    • 0038094854 scopus 로고
    • First passage percolation on the square lattice. I
    • SMYTHE, R. T. and WIERMAN, J. C. (1977). First passage percolation on the square lattice. I. Adv. in Appl. Probab. 9 38-54.
    • (1977) Adv. in Appl. Probab. , vol.9 , pp. 38-54
    • Smythe, R.T.1    Wierman, J.C.2
  • 11
    • 0037757165 scopus 로고
    • First passage percolation on the square lattice
    • Springer, New York
    • SMYTHE, R. T. and WIERMAN, J. C. (1978). First Passage Percolation on the Square Lattice. Lecture Notes in Math. 671. Springer, New York.
    • (1978) Lecture Notes in Math. , vol.671
    • Smythe, R.T.1    Wierman, J.C.2
  • 12
    • 0038094853 scopus 로고
    • On conjectures in first-passage percolation theory
    • WIERMAN, J. and REH, W. (1978). On conjectures in first-passage percolation theory. Ann. Probab. 6 388-397.
    • (1978) Ann. Probab. , vol.6 , pp. 388-397
    • Wierman, J.1    Reh, W.2
  • 13
    • 0037757163 scopus 로고
    • 0n/n in first-passage percolation
    • 0n/n in first-passage percolation. Ann. Probab. 12 1068-1076.
    • (1984) Ann. Probab. , vol.12 , pp. 1068-1076
    • Zhang, Y.1    Zhang, Y.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.