publication . Preprint . 2014

Universality of two-dimensional critical cellular automata

Bollobás, Béla; Duminil-Copin, Hugo; Morris, Robert; Smith, Paul;
Open Access English
  • Published: 25 Jun 2014
Comment: 83 pages, 9 figures. This version contains significant changes to Section 8, correcting an error in the proof, and numerous additional minor changes
free text keywords: Mathematics - Probability, Mathematics - Combinatorics
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Foundational Research on MULTIlevel comPLEX networks and systems
  • Funder: European Commission (EC)
  • Project Code: 317532
  • Funding stream: FP7 | SP1 | ICT
NSF| Random Geometric Graphs
  • Funder: National Science Foundation (NSF)
  • Project Code: 1301614
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
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30 references, page 1 of 2

1. M. Aizenman and J.L. Lebowitz, Metastability effects in bootstrap percolation, J. Phys. A 21 (1988), no. 19, 3801-3813. [OpenAIRE]

2. P. Balister, B. Bollob´as, M.J. Przykucki, and P.J. Smith, Subcritical neighbourhood family percolation models have non-trivial phase transitions, Preprint, arXiv:1311.5883.

3. J. Balogh, B. Bollob´as, H. Duminil-Copin, and R. Morris, The sharp threshold for bootstrap percolation in all dimensions, Trans. Amer. Math. Soc. 364 (2012), no. 5, 2667-2701. [OpenAIRE]

4. J. Balogh, B. Bollob´as, and R. Morris, Bootstrap percolation in three dimensions, Ann. Probab. 37 (2009), no. 4, 1329-1380.

5. , Majority bootstrap percolation on the hypercube, Combin. Probab. Comput. 18 (2009), no. 1-2, 17-51.

6. , Bootstrap percolation in high dimensions, Combin. Probab. Comput. 19 (2010), no. 5- 6, 643-692.

7. J. Balogh, Y. Peres, and G. Pete, Bootstrap percolation on infinite trees and non-amenable groups, Combin. Probab. Comput. 15 (2006), no. 2, 715-730.

8. J. Balogh and B. Pittel, Bootstrap percolation on the random regular graph, Random Structures Algorithms 30 (2007), no. 1-2, 257-286.

9. T. Bohman, Discrete threshold growth dynamics are omnivorous for box neighborhoods, Trans. Amer. Math. Soc. 351 (1999), no. 3, 947-983.

10. B. Bollob´as, K. Gunderson, C. Holmgren, S. Janson, and M. Przykucki, Bootstrap percolation on Galton-Watson trees, Preprint, arXiv:1304.2260.

11. B. Bollob´as and O. Riordan, Percolation, Cambridge, 2006.

12. B. Bollob´as, P.J. Smith, and A.J. Uzzell, Monotone cellular automata in a random environment, To appear, Combin. Probab. Comput.

13. K. Bringmann and K. Mahlburg, Improved bounds on metastability thresholds and probabilities for generalized bootstrap percolation, Trans. Amer. Math. Soc. 364 (2012), 3829-3859.

14. K. Bringmann, K. Mahlburg, and A. Mellit, Convolution bootstrap percolation models, Markovtype stochastic processes, and mock theta functions, Int. Math. Res. Not. 5 (2013), 971-1013. [OpenAIRE]

15. R. Cerf and E.N.M. Cirillo, Finite size scaling in three-dimensional bootstrap percolation, Ann. Probab. 27 (1999), no. 4, 1837-1850.

30 references, page 1 of 2
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