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Volumn 9, Issue , 2004, Pages 710-769

Gaussian scaling for the critical spread-out contact process above the upper critical dimension

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EID: 8744247449     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v9-224     Document Type: Article
Times cited : (23)

References (34)
  • 1
    • 0001639861 scopus 로고
    • Tree graph inequalities and critical behavior in percolation models
    • M. Aizenman and C. M. Newman. Tree graph inequalities and critical behavior in percolation models. J. Statist. Phys. 36 (1984): 107-143.
    • (1984) J. Statist. Phys. , vol.36 , pp. 107-143
    • Aizenman, M.1    Newman, C.M.2
  • 2
    • 0000699765 scopus 로고
    • Percolation critical exponents under the triangle condition
    • D. J. Barsky and M. Aizenman. Percolation critical exponents under the triangle condition. Ann. Probab. 19 (1991): 1520-1536.
    • (1991) Ann. Probab. , vol.19 , pp. 1520-1536
    • Barsky, D.J.1    Aizenman, M.2
  • 3
    • 0032047357 scopus 로고    scopus 로고
    • Critical exponents for the contact process under the triangle condition
    • D. J. Barsky and C. C. Wu. Critical exponents for the contact process under the triangle condition. J. Statist. Phys. 91 (1998): 95-124.
    • (1998) J. Statist. Phys. , vol.91 , pp. 95-124
    • Barsky, D.J.1    Wu, C.C.2
  • 4
    • 0000236076 scopus 로고
    • Exponential decay for subcritical contact and percolation processes
    • C. Bezuidenhout and G. Grimmett. Exponential decay for subcritical contact and percolation processes. Ann. Probab. 19 (1991): 984-1009.
    • (1991) Ann. Probab. , vol.19 , pp. 984-1009
    • Bezuidenhout, C.1    Grimmett, G.2
  • 5
    • 8744262248 scopus 로고    scopus 로고
    • Strong pointwise estimates for the weakly self-avoiding walk
    • To appear in
    • E. Bolthausen and C. Ritzmann. Strong pointwise estimates for the weakly self-avoiding walk. To appear in Ann. Probab.
    • Ann. Probab
    • Bolthausen, E.1    Ritzmann, C.2
  • 7
    • 0001405289 scopus 로고
    • Self-avoiding walk in 5 or more dimensions
    • D.C. Brydges and T. Spencer. Self-avoiding walk in 5 or more dimensions. Commun. Math. Phys., 97 (1985):125-148.
    • (1985) Commun. Math. Phys. , vol.97 , pp. 125-148
    • Brydges, D.C.1    Spencer, T.2
  • 8
    • 0038979178 scopus 로고    scopus 로고
    • Rescaled contact processes converge to super-Brownian motion in two or more dimensions
    • R. Durrett and E. Perkins. Rescaled contact processes converge to super-Brownian motion in two or more dimensions. Probab. Th. Rel. Fields 114 (1999): 309-399.
    • (1999) Probab. Th. Rel. Fields , vol.114 , pp. 309-399
    • Durrett, R.1    Perkins, E.2
  • 10
    • 0002977776 scopus 로고    scopus 로고
    • Directed percolation and random walk
    • V. Sidoravicius). Birkhauser
    • G. Grimmett and P. Hiemer. Directed percolation and random walk. In and Out of Equilibrium (ed., V. Sidoravicius). Birkhauser (2002): 273-297.
    • (2002) and out of Equilibrium , pp. 273-297
    • Grimmett, G.1    Hiemer, P.2
  • 11
    • 34249952953 scopus 로고
    • Mean-field critical behaviour for percolation in high dimensions
    • T. Hara and G. Slade. Mean-field critical behaviour for percolation in high dimensions. Commun. Math. Phys., 128 (1990):333-391.
    • (1990) Commun. Math. Phys. , vol.128 , pp. 333-391
    • Hara, T.1    Slade, G.2
  • 12
    • 0038999790 scopus 로고
    • Self-avoiding walk in five or more dimensions. I. The critical behaviour
    • T. Hara and G. Slade. Self-avoiding walk in five or more dimensions. I. The critical behaviour. Commun. Math. Phys., 147 (1992):101-136.
    • (1992) Commun. Math. Phys. , vol.147 , pp. 101-136
    • Hara, T.1    Slade, G.2
  • 13
    • 0034336207 scopus 로고    scopus 로고
    • The scaling limit of the incipient infinite cluster in high-dimensional percolation. I. Critical exponents
    • T. Hara and G. Slade. The scaling limit of the incipient infinite cluster in high-dimensional percolation. I. Critical exponents. J. Statist. Phys. 99 (2000): 1075-1168.
    • (2000) J. Statist. Phys. , vol.99 , pp. 1075-1168
    • Hara, T.1    Slade, G.2
  • 14
    • 0034345450 scopus 로고    scopus 로고
    • The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion
    • T. Hara and G. Slade. The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion. J. Math. Phys. 41 (2000): 1244-1293.
    • (2000) J. Math. Phys. , vol.41 , pp. 1244-1293
    • Hara, T.1    Slade, G.2
  • 15
    • 0032094569 scopus 로고    scopus 로고
    • A new inductive approach to the lace expansion for self-avoiding walks
    • R. van der Hofstad, F. den Hollander and G. Slade. A new inductive approach to the lace expansion for self-avoiding walks. Probab. Th. Rel. Fields 111 (1998): 253-286.
    • (1998) Probab. Th. Rel. Fields , vol.111 , pp. 253-286
    • Van Der Hofstad, R.1    Den Hollander, F.2    Slade, G.3
  • 16
    • 0036882738 scopus 로고    scopus 로고
    • Construction of the incipient infinite cluster for the spread-out oriented percolation above 4+1 dimensions
    • R. van der Hofstad, F. den Hollander and G. Slade. Construction of the incipient infinite cluster for the spread-out oriented percolation above 4+1 dimensions. Commun. Math. Phys. 231 (2002): 435-461.
    • (2002) Commun. Math. Phys. , vol.231 , pp. 435-461
    • Van Der Hofstad, R.1    Den Hollander, F.2    Slade, G.3
  • 18
    • 85037890596 scopus 로고    scopus 로고
    • Convergence of the critical finite-range contact process to super-Brownian motion above 4 spatial dimensions
    • R. van der Hofstad and A. Sakai. Convergence of the critical finite-range contact process to super-Brownian motion above 4 spatial dimensions. In preparation.
    • Preparation
    • Van Der Hofstad, R.1    Sakai, A.2
  • 19
    • 0036004916 scopus 로고    scopus 로고
    • A generalised inductive approach to the lace expansion
    • R. van der Hofstad and G. Slade. A generalised inductive approach to the lace expansion. Probab. Th. Rel. Fields 122 (2002): 389-430.
    • (2002) Probab. Th. Rel. Fields , vol.122 , pp. 389-430
    • Van Der Hofstad, R.1    Slade, G.2
  • 20
    • 0037402965 scopus 로고    scopus 로고
    • Convergence of critical oriented percolation to super-Brownian motion above 4+1 dimensions
    • R. van der Hofstad and G. Slade. Convergence of critical oriented percolation to super-Brownian motion above 4+1 dimensions. Ann. Inst. H. Poincare Probab. Statist. 39 (2003): 413-485.
    • (2003) Ann. Inst. H. Poincare Probab. Statist. , vol.39 , pp. 413-485
    • Van Der Hofstad, R.1    Slade, G.2
  • 21
    • 0038286482 scopus 로고    scopus 로고
    • The lace expansion on a tree with application to networks of self-avoiding walks
    • R. van der Hofstad and G. Slade. The lace expansion on a tree with application to networks of self-avoiding walks. Adv. Appl. Math. 30 (2003): 471-528.
    • (2003) Adv. Appl. Math. , vol.30 , pp. 471-528
    • Van Der Hofstad, R.1    Slade, G.2
  • 24
    • 0000553017 scopus 로고
    • Triangle condition for oriented percolation in high dimensions
    • B. G. Nguyen and W.-S. Yang. Triangle condition for oriented percolation in high dimensions. Ann. Probab. 21 (1993): 1809-1844.
    • (1993) Ann. Probab. , vol.21 , pp. 1809-1844
    • Nguyen, B.G.1    Yang, W.-S.2
  • 25
    • 21844520722 scopus 로고
    • Gaussian limit for critical oriented percolation in high dimensions
    • B. G. Nguyen and W.-S. Yang. Gaussian limit for critical oriented percolation in high dimensions. J. Statist. Phys. 78 (1995): 841-876.
    • (1995) J. Statist. Phys. , vol.78 , pp. 841-876
    • Nguyen, B.G.1    Yang, W.-S.2
  • 27
    • 0035535108 scopus 로고    scopus 로고
    • Mean-field critical behavior for the contact process
    • A. Sakai. Mean-field critical behavior for the contact process. J. Statist. Phys. 104 (2001): 111-143.
    • (2001) J. Statist. Phys. , vol.104 , pp. 111-143
    • Sakai, A.1
  • 28
    • 0036110110 scopus 로고    scopus 로고
    • Hyperscaling inequalities for the contact process and oriented percolation
    • A. Sakai. Hyperscaling inequalities for the contact process and oriented percolation. J. Statist. Phys. 106 (2002): 201-211.
    • (2002) J. Statist. Phys. , vol.106 , pp. 201-211
    • Sakai, A.1
  • 29
    • 0032023976 scopus 로고    scopus 로고
    • The triangle condition for contact processes on homogeneous trees
    • R. Schonmann. The triangle condition for contact processes on homogeneous trees. J. Statist. Phys. 90 (1998): 1429-1440.
    • (1998) J. Statist. Phys. , vol.90 , pp. 1429-1440
    • Schonmann, R.1
  • 30
    • 27644432962 scopus 로고
    • The diffusion of self-avoiding random walk in high dimensions
    • G. Slade. The diffusion of self-avoiding random walk in high dimensions. Commun. Math. Phys., 110 (1987): 661-683.
    • (1987) Commun. Math. Phys. , vol.110 , pp. 661-683
    • Slade, G.1
  • 31
    • 33646972718 scopus 로고
    • Convergence of self-avoiding random walk to Brownian motion in high dimensions
    • G. Slade. Convergence of self-avoiding random walk to Brownian motion in high dimensions. J. Phys. A: Math. Gen., 21 (1988):L417-L420.
    • (1988) J. Phys. A: Math. Gen. , vol.21 , pp. L417-L420
    • Slade, G.1
  • 32
    • 0010851861 scopus 로고
    • The lace expansion and the upper critical dimension for percolation
    • G. Slade. The lace expansion and the upper critical dimension for percolation. Lectures in Applied Mathematics 27 (1991):53-63.
    • (1991) Lectures in Applied Mathematics , vol.27 , pp. 53-63
    • Slade, G.1
  • 34
    • 0002988718 scopus 로고
    • The contact process on a tree: Behavior near the first phase transition
    • C. C. Wu. The contact process on a tree: Behavior near the first phase transition. Stochastic Process. Appl. 57 (1995): 99-112.
    • (1995) Stochastic Process. Appl. , vol.57 , pp. 99-112
    • Wu, C.C.1


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