Given enough choice, simple local rules percolate discontinuously

European Physical Journal B

Volumn 87, Issue 12, 2014, Pages

  Waagen, Alex ^a   D’Souza, Raissa M ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b SANTA FE INSTITUTE   (United States)

Author keywords

Statistical and Nonlinear Physics

Indexed keywords

EVOLUTIONARY ALGORITHMS; PERCOLATION (FLUIDS); PERCOLATION (SOLID STATE); STATISTICAL PHYSICS;

COMPONENT SIZE; DISCONTINUOUS TRANSITION; EVOLUTION ALGORITHMS; FINITE SYSTEMS; GIANT COMPONENTS; PERCOLATION TRANSITION; STATISTICAL AND NONLINEAR PHYSICS; THERMODYNAMIC LIMITS;

SOLVENTS;

EID: 84919904523     PISSN: 14346028     EISSN: 14346036     Source Type: Journal    
DOI: 10.1140/epjb/e2014-50278-x     Document Type: Article

References (30)

1. D. Stauffer, Introduction to percolation theory (Taylor & Francis, 1985)
2. M.E.J. Newman, D.J. Watts, Phys. Rev. E 60, 7332 (1999)
3. R. Cohen, K. Erez, D. ben Avraham, S. Havlin, Phys. Rev. Lett. 85, 4626 (2000)
4. D.S. Callaway, M.E.J. Newman, S.H. Strogatz, D.J. Watts, Phys. Rev. Lett. 85, 5468 (2000)
5. C. Moore, M.E.J. Newman, Phys. Rev. E 61, 5678 (2000)
6. M.E.J. Newman, Networks: An Introduction (Oxford University Press, New York, 2010)
7. O. Riordan, L. Warnke, Ann. Appl. Probab. 22, 1450 (2012)
8. Y. Azar, A.Z. Broder, A.R. Karlin, E. Upfal, SIAM J. Comput. 29, 180 (1999)
9. M. Mitzenmacher, A.W. Richa, R. Sitaraman, in Handbook of Randomized Computing (Kluwer, 2000), pp. 255–312
10. M. Mitzenmacher, IEEE Trans. Parallel Distrib. Syst. 12, 1094 (2001)
11. A. Sinclair, D. Vilenchik, Delaying satisfiability for random 2SAT, in Proceedings of the 13th International Conference on Approximation, and 14th International Conference on Randomization, and combinatorial optimization: algorithms and techniques (Springer-Verlag, Berlin, Heidelberg, 2010), pp. 710–723
12. T. Bohman, A. Frieze, Random Struct. Algorithms 19, 75 (2001)
13. D. Achlioptas, R.M. D’Souza, J. Spencer, Science 323, 1453 (2009)
14. R.A. da Costa, S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes, Phys. Rev. Lett. 105, 255701 (2010)
15. J. Nagler, A. Levina, M. Timme, Nat. Phys. 7, 265 (2011)
16. P. Grassberger, C. Christensen, G. Bizhani, S.W. Son, M. Paczuski, Phys. Rev. Lett. 106, 225701 (2011)
17. S.S. Manna, A. Chatterjee, Physica A 390, 177 (2011)
18. H.K. Lee, B.J. Kim, H. Park, Phys. Rev. E 84, 020101 (2011)
19. L. Tian, D.N. Shi, Phys. Lett. A 376, 286 (2012)
20. O. Riordan, L. Warnke, Science 333, 322 (2011)
21. W. Chen, R.M. D’Souza, Phys. Rev. Lett. 106, 115701 (2011)
22. K. Panagiotou, R. Spöhel, A. Steger, H. Thomas, Electron. Notes Discrete Math. 38, 699 (2011)
23. J. Nagler, T. Tiessen, H.W. Gutch, Phys. Rev. X 2, 031009 (2012)
24. H. Hwang, J. Herrmann, Y. Cho, B. Kahng, Science 339, 1185 (2013)
25. J. Spencer, N. Wormald, Combinatorica 27, 587 (2007)
26. S. Janson, J. Spencer, arXiv:1005.4494v1 [math.CO] (2012)
27. P. Erdős, A. Rényi, Magyar Tud. Akad. Mat. Kutató Int. Közl 5, 17 (1960)
28. R. Durrett, Probability: Theory and Examples, Cambridge Series in Statistical and Probabilistic Mathematics (Cambridge University Press, 2010)
29. E.J. Friedman, A.S. Landsberg, Phys. Rev. Lett. 103, 255701 (2009)
30. D. Aldous, Bernoulli 5, 3 (1999)