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Volumn 26, Issue 3, 1998, Pages 1232-1250

Exact limiting shape for a simplified model of first-passage percolation on the plane

Author keywords

Asymptotic shape; First passage percolation; Hydrodynamic limit; Tagged particle

Indexed keywords


EID: 0032361582     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1022855751     Document Type: Article
Times cited : (61)

References (24)
  • 1
    • 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
  • 2
    • 0031514908 scopus 로고    scopus 로고
    • Approximation of subadditive functions and convergence rates in limiting-shape results
    • ALEXANDER, K. S. (1997). Approximation of subadditive functions and convergence rates in limiting-shape results. Ann. Probab. 25 30-55.
    • (1997) Ann. Probab. , vol.25 , pp. 30-55
    • Alexander, K.S.1
  • 3
    • 0001324581 scopus 로고
    • On Hopf's formulas for solutions of Hamilton-Jacobi equations
    • BARDI, M. and EVANS, L. C. (1984). On Hopf's formulas for solutions of Hamilton-Jacobi equations. Nonlinear Anal. 8 1373-1381.
    • (1984) Nonlinear Anal. , vol.8 , pp. 1373-1381
    • Bardi, M.1    Evans, L.C.2
  • 4
    • 0000632378 scopus 로고
    • First-passage percolation: The stationary case
    • BOIVIN, D. (1990). First-passage percolation: the stationary case. Probab. Theory Related Fields 86 491-499.
    • (1990) Probab. Theory Related Fields , vol.86 , pp. 491-499
    • Boivin, D.1
  • 5
    • 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
  • 6
    • 0013523416 scopus 로고
    • The shape of the limit set in Richardson's growth model
    • DURRETT, R. and LIGGETT, T. (1981). The shape of the limit set in Richardson's growth model. Ann. Probab. 9 186-193.
    • (1981) Ann. Probab. , vol.9 , pp. 186-193
    • Durrett, R.1    Liggett, T.2
  • 7
    • 0000102847 scopus 로고
    • Some Min-Max methods for the Hamilton-Jacobi equation
    • EVANS, L. C. (1984). Some Min-Max methods for the Hamilton-Jacobi equation. Indiana Univ. Math. J. 33 31-50.
    • (1984) Indiana Univ. Math. J. , vol.33 , pp. 31-50
    • Evans, L.C.1
  • 10
    • 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-Bayes-Laplace Anniversary Volume (J. Neyman and L. Le Cam, eds.) 61-110. Springer, Berlin.
    • (1965) Bernoulli-Bayes-Laplace Anniversary Volume , pp. 61-110
    • Hammersley, J.M.1    Welsh, D.J.A.2
  • 11
    • 21344460228 scopus 로고
    • Asymptotic shapes for stationary first-passage percolation
    • HÄGGSTRÖM, O. and MEESTER, R. (1995). Asymptotic shapes for stationary first-passage percolation. Ann. Probab. 23 1511-1522.
    • (1995) Ann. Probab. , vol.23 , pp. 1511-1522
    • Häggström, O.1    Meester, R.2
  • 12
    • 0031532659 scopus 로고    scopus 로고
    • Euclidean models of first-passage percolation
    • HOWARD, C. D. and NEWMAN, C. M. (1997). Euclidean models of first-passage percolation. Probab. Theory Related Fields 108 153-170.
    • (1997) Probab. Theory Related Fields , vol.108 , pp. 153-170
    • Howard, C.D.1    Newman, C.M.2
  • 13
    • 0000264803 scopus 로고
    • Aspects of first-passage percolation
    • Springer, Berlin
    • KESTEN, H. (1986). Aspects of first-passage percolation. Lecture Notes in Math. 1180 125-264. Springer, Berlin.
    • (1986) Lecture Notes in Math. , vol.1180 , pp. 125-264
    • Kesten, H.1
  • 14
    • 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
  • 15
    • 0001656464 scopus 로고
    • The ergodic theory of subadditive stochastic processes
    • KINGMAN, J. F. C. (1968). The ergodic theory of subadditive stochastic processes. J. Royal Statist. Soc. Ser. B 30 499-510.
    • (1968) J. Royal Statist. Soc. Ser. B , vol.30 , pp. 499-510
    • Kingman, J.F.C.1
  • 16
    • 0000061720 scopus 로고
    • Central limit theorems for infinite series of queues and applications to simple exclusion
    • KIPNIS, C. (1986). Central limit theorems for infinite series of queues and applications to simple exclusion. Ann. Probab. 14 397-408.
    • (1986) Ann. Probab. , vol.14 , pp. 397-408
    • Kipnis, C.1
  • 18
    • 0001754757 scopus 로고
    • Divergence of shape fluctuations in two dimensions
    • NEWMAN, C. M. and PIZA, M. S. T. (1995). Divergence of shape fluctuations in two dimensions. Ann. Probab. 23 977-1005.
    • (1995) Ann. Probab. , vol.23 , pp. 977-1005
    • Newman, C.M.1    Piza, M.S.T.2
  • 19
    • 21844504694 scopus 로고
    • Evolution of tagged particles in non-reversible particle systems
    • REZAKHANLOU, F. (1994). Evolution of tagged particles in non-reversible particle systems. Comm. Math. Phys. 165 1-32.
    • (1994) Comm. Math. Phys. , vol.165 , pp. 1-32
    • Rezakhanlou, F.1
  • 21
    • 0000528853 scopus 로고
    • A limit theorem for the position of a tagged particle in a simple exclusion process
    • SAADA, E. (1987). A limit theorem for the position of a tagged particle in a simple exclusion process. Ann. Probab. 15 375-381.
    • (1987) Ann. Probab. , vol.15 , pp. 375-381
    • Saada, E.1
  • 22
    • 3042554249 scopus 로고    scopus 로고
    • A microscopic model for the Burgers equation and longest increasing subsequences
    • SEPPÄLÄINEN, T. (1996). A microscopic model for the Burgers equation and longest increasing subsequences. Electronic J. Probab. 1 1-51.
    • (1996) Electronic J. Probab. , vol.1 , pp. 1-51
    • Seppäläinen, T.1
  • 23
    • 0001969192 scopus 로고    scopus 로고
    • Hydrodynamic scaling, convex duality, and asymptotic shapes of growth models
    • SEPPÄLÄINEN, T. (1998). Hydrodynamic scaling, convex duality, and asymptotic shapes of growth models. Markov Processes Related Fields 4 1-26.
    • (1998) Markov Processes Related Fields , vol.4 , pp. 1-26
    • Seppäläinen, T.1
  • 24
    • 0001820948 scopus 로고
    • A shape result for first-passage percolation on the Voronoi tessellation and Delaunay triangulation
    • (A. Frieze and T. Luczak, eds.) Wiley, New York.
    • VAHIDI-ASL, M. Q. and WIERMAN, J. (1992). A shape result for first-passage percolation on the Voronoi tessellation and Delaunay triangulation. In Random Graphs 2 (A. Frieze and T. Luczak, eds.) 247-262. Wiley, New York.
    • (1992) Random Graphs , vol.2 , pp. 247-262
    • Vahidi-Asl, M.Q.1    Wierman, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.