The survival probability for critical spread-out oriented percolation above 4 + 1 dimensions. II. Expansion

Remco Van der Hofstad; Frank den Hollander; Gordon Slade

Annales de l'I.H.P. Probabilités et statistiques (2007)

  • Volume: 43, Issue: 5, page 509-570
  • ISSN: 0246-0203

How to cite

top

Van der Hofstad, Remco, den Hollander, Frank, and Slade, Gordon. "The survival probability for critical spread-out oriented percolation above $4+1$ dimensions. II. Expansion." Annales de l'I.H.P. Probabilités et statistiques 43.5 (2007): 509-570. <http://eudml.org/doc/77945>.

@article{VanderHofstad2007,
author = {Van der Hofstad, Remco, den Hollander, Frank, Slade, Gordon},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {oriented percolation; lace expansion; survival probability; critical exponent; nonlinear recursion},
language = {eng},
number = {5},
pages = {509-570},
publisher = {Elsevier},
title = {The survival probability for critical spread-out oriented percolation above $4+1$ dimensions. II. Expansion},
url = {http://eudml.org/doc/77945},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Van der Hofstad, Remco
AU - den Hollander, Frank
AU - Slade, Gordon
TI - The survival probability for critical spread-out oriented percolation above $4+1$ dimensions. II. Expansion
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2007
PB - Elsevier
VL - 43
IS - 5
SP - 509
EP - 570
LA - eng
KW - oriented percolation; lace expansion; survival probability; critical exponent; nonlinear recursion
UR - http://eudml.org/doc/77945
ER -

References

top
  1. [1] D.J. Barsky, M. Aizenman, Percolation critical exponents under the triangle condition, Ann. Probab.19 (1991) 1520-1536. Zbl0747.60093MR1127713
  2. [2] C. Bezuidenhout, G. Grimmett, The critical contact process dies out, Ann. Probab.18 (1990) 1462-1482. Zbl0718.60109MR1071804
  3. [3] G. Grimmett, Percolation, second ed., Springer, Berlin, 1999. Zbl0926.60004MR1707339
  4. [4] G. Grimmett, P. Hiemer, Directed percolation and random walk, in: Sidoravicius V. (Ed.), In and Out of Equilibrium, Birkhäuser, Boston, 2002, pp. 273-297. Zbl1010.60087MR1901958
  5. [5] T. Hara, G. Slade, Mean-field critical behaviour for percolation in high dimensions, Comm. Math. Phys.128 (1990) 333-391. Zbl0698.60100MR1043524
  6. [6] T. Hara, G. Slade, The scaling limit of the incipient infinite cluster in high-dimensional percolation. I. Critical exponents, J. Stat. Phys.99 (2000) 1075-1168. Zbl0968.82016MR1773141
  7. [7] R. van der Hofstad, F. den Hollander, G. Slade, The survival probability for critical spread-out oriented percolation above 4 + 1 dimensions. I. Induction. Preprint, 2005. Probab. Theory Related Fields, in press. Zbl1130.60094MR2299712
  8. [8] R. van der Hofstad, F. den Hollander, G. Slade, Construction of the incipient infinite cluster for spread-out oriented percolation above 4 + 1 dimensions, Comm. Math. Phys.231 (2002) 435-461. Zbl1013.82017MR1946445
  9. [9] R. van der Hofstad, A. Sakai, Gaussian scaling for the critical spread-out contact process above the upper critical dimension, Electron. J. Probab.9 (2004) 710-769. Zbl1077.60076MR2110017
  10. [10] R. van der Hofstad, A. Sakai, Critical points for spread-out self-avoiding walk, percolation and the contact process, Probab. Theory Related Fields132 (2005) 438-470. Zbl1083.60080MR2197108
  11. [11] R. van der Hofstad, A. Sakai, Convergence of the critical finite-range contact process to super-Brownian motion above the upper critical dimension. I. The higher-point functions, in preparation. Zbl1226.60139
  12. [12] R. van der Hofstad, 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. Zbl1226.60139
  13. [13] R. van der Hofstad, G. Slade, A generalised inductive approach to the lace expansion, Probab. Theory Related Fields122 (2002) 389-430. Zbl1002.60095MR1892852
  14. [14] R. van der Hofstad, G. Slade, Convergence of critical oriented percolation to super-Brownian motion above 4 + 1 dimensions, Ann. Inst. H. Poincaré Probab. Statist.39 (2003) 415-485. Zbl1020.60099MR1978987
  15. [15] N. Madras, G. Slade, The Self-Avoiding Walk, Birkhäuser, Boston, 1993. Zbl0780.60103MR1197356
  16. [16] B.G. Nguyen, W.-S. Yang, Triangle condition for oriented percolation in high dimensions, Ann. Probab.21 (1993) 1809-1844. Zbl0806.60097MR1245291
  17. [17] A. Sakai, Mean-field critical behavior for the contact process, J. Stat. Phys.104 (2001) 111-143. Zbl1019.82012MR1851386
  18. [18] G. Slade, The Lace Expansion and its Applications, Lecture Notes in Mathematics, vol. 1879, Springer, 2006, Ecole d'Eté Probabilit. Saint-Flour. Zbl1113.60005MR2239599

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.