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References

  1. Aizenman, Michael; Newman, Charles M. Tree graph inequalities and critical behavior in percolation models. J. Statist. Phys. 36 (1984), no. 1-2, 107--143. MR0762034 (86h:82045)
  2. Bezuidenhout, Carol; Grimmett, Geoffrey. Exponential decay for subcritical contact and percolation processes. Ann. Probab. 19 (1991), no. 3, 984--1009. MR1112404 (92k:60218)
  3. Chen, Lung-Chi; Sakai, Akira. Critical behavior and the limit distribution for long-range oriented percolation. I. Probab. Theory Related Fields 142 (2008), no. 1-2, 151--188. MR2413269 (2009h:60161)
  4. Chen, Lung-Chi; Sakai, Akira. Critical behavior and the limit distribution for long-range oriented percolation. I. Probab. Theory Related Fields 142 (2008), no. 1-2, 151--188. MR2413269 (2009h:60161)
  5. Durrett, Richard; Perkins, Edwin A. Rescaled contact processes converge to super-Brownian motion in two or more dimensions. Probab. Theory Related Fields 114 (1999), no. 3, 309--399. MR1705115 (2000f:60149)
  6. A.M. Etheridge. An Introduction to Superprocesses. American Mathematical Society, Providence, (2000).
  7. G. Grimmett. Percolation. Springer, Berlin (1999). MR1707339
  8. Grimmett, Geoffrey; Hiemer, Philipp. Directed percolation and random walk. In and out of equilibrium (Mambucaba, 2000), 273--297, Progr. Probab., 51, Birkhäuser Boston, Boston, MA, 2002. MR1901958 (2003b:60159)
  9. Hara, Takashi; Slade, Gordon. Mean-field critical behaviour for percolation in high dimensions. Comm. Math. Phys. 128 (1990), no. 2, 333--391. MR1043524 (91a:82037)
  10. Hara, Takashi; Slade, Gordon. The scaling limit of the incipient infinite cluster in high-dimensional percolation. I. Critical exponents. J. Statist. Phys. 99 (2000), no. 5-6, 1075--1168. MR1773141 (2001g:82053a)
  11. Hara, Takashi; Slade, Gordon. The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion.Probabilistic techniques in equilibrium and nonequilibrium statistical physics. J. Math. Phys. 41 (2000), no. 3, 1244--1293. MR1757958 (2001g:82053b)
  12. van der Hofstad, Remco. Spread-out oriented percolation and related models above the upper critical dimension: induction and superprocesses. On the nature of isotherms at first order phase transitions for classical lattice models. Spread-out oriented percolation and related models above the upper critical dimension: induction and superprocesses, 91--181 (electronic), Ensaios Mat., 9, Soc. Brasil. Mat., Rio de Janeiro, 2005. MR2209700 (2007a:82022)
  13. van der Hofstad, Remco. Infinite canonical super-Brownian motion and scaling limits. Comm. Math. Phys. 265 (2006), no. 3, 547--583. MR2231682 (2007d:60050)
  14. van der Hofstad, Remco; den Hollander, Frank; Slade, Gordon. A new inductive approach to the lace expansion for self-avoiding walks. Probab. Theory Related Fields 111 (1998), no. 2, 253--286. MR1633582 (99j:82043)
  15. van der Hofstad, Remco; den Hollander, Frank; Slade, Gordon. Construction of the incipient infinite cluster for spread-out oriented percolation above $4+1$ dimensions. Comm. Math. Phys. 231 (2002), no. 3, 435--461. MR1946445 (2003j:60141)
  16. R. van der Hofstad, F. den Hollander, and G. Slade. The survival probability for critical spread-out oriented percolation above $4+1$ dimensions. I. Induction. Probab. Theory Related Fields, 138(2007): 363--389. MR2299712
  17. van der Hofstad, Remco; den Hollander, Frank; Slade, Gordon. The survival probability for critical spread-out oriented percolation above $4+1$ dimensions. II. Expansion. Ann. Inst. H. Poincaré Probab. Statist. 43 (2007), no. 5, 509--570. MR2347096 (2009d:60326)
  18. van der Hofstad, Remco; Sakai, Akira. Gaussian scaling for the critical spread-out contact process above the upper critical dimension. Electron. J. Probab. 9 (2004), no. 24, 710--769 (electronic). MR2110017 (2006b:60221)
  19. R. van der Hofstad and A. Sakai. Critical points for spread-out contact processes and oriented percolation. Probab. Theory Relat. Fields, bf 132 (2005): 438--470. MR2197108
  20. R. van der Hofstad and A. Sakai. Convergence of the critical finite-range contact process to super-Brownian motion above the upper critical dimension. II. The survival probability. In preparation.
  21. van der Hofstad, Remco; Slade, Gordon. A generalised inductive approach to the lace expansion. Probab. Theory Related Fields 122 (2002), no. 3, 389--430. MR1892852 (2003g:60168)
  22. van der Hofstad, Remco; Slade, Gordon. Convergence of critical oriented percolation to super-Brownian motion above $4+1$ dimensions. Ann. Inst. H. Poincaré Probab. Statist. 39 (2003), no. 3, 413--485. MR1978987 (2004a:60158)
  23. van der Hofstad, Remco; Slade, Gordon. The lace expansion on a tree with application to networks of self-avoiding walks. Adv. in Appl. Math. 30 (2003), no. 3, 471--528. MR1973954 (2004m:82053)
  24. M.P. Holmes. Convergence of lattice trees to super-Brownian motion above the critical dimension. Electron. J. Probab.13 (2008): 671--755. MR2399294
  25. Holmes, Mark; Perkins, Edwin. Weak convergence of measure-valued processes and $r$-point functions. Ann. Probab. 35 (2007), no. 5, 1769--1782. MR2349574 (2008g:60150)
  26. Liggett, Thomas M. Stochastic interacting systems: contact, voter and exclusion processes.Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 324. Springer-Verlag, Berlin, 1999. xii+332 pp. ISBN: 3-540-65995-1 MR1717346 (2001g:60247)
  27. Sakai, Akira. Mean-field critical behavior for the contact process. J. Statist. Phys. 104 (2001), no. 1-2, 111--143. MR1851386 (2003f:82070)
  28. Sakai, Akira. Hyperscaling inequalities for the contact process and oriented percolation. J. Statist. Phys. 106 (2002), no. 1-2, 201--211. MR1881726 (2003a:82037)
  29. A. Sakai. Lace expansion for the Ising model. Comm. Math. Phys.272 (2007): 283--344. MR2300246
  30. Slade, Gordon. Scaling limits and super-Brownian motion. Notices Amer. Math. Soc. 49 (2002), no. 9, 1056--1067. MR1927455 (2003g:60170)
  31. Slade, G. The lace expansion and its applications.Lectures from the 34th Summer School on Probability Theory held in Saint-Flour, July 6--24, 2004.Edited and with a foreword by Jean Picard.Lecture Notes in Mathematics, 1879. Springer-Verlag, Berlin, 2006. xiv+228 pp. ISBN: 978-3-540-31189-8; 3-540-31189-0 MR2239599 (2007m:60301)
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