Achlioptas process phase transitions are continuous

Annals of Applied Probability

Volumn 22, Issue 4, 2012, Pages 1450-1464

  Riordan, Oliver ^a   Warnke, Lutz ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Achlioptas processes; Explosive percolation; Random graphs

Indexed keywords

EID: 84870935529     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-AAP798     Document Type: Article

References (16)

1. ACHLIOPTAS, D., D'SOUZA, R. M. and SPENCER, J. (2009). Explosive percolation in random networks. Science 323 1453-1455. MR2502843
2. BOHMAN, T. (2009). Emergence of connectivity in networks. Science 323 1438-1439.
3. BOHMAN, T. and FRIEZE, A. (2001). Avoiding a giant component. Random Structures Algorithms 19 75-85. MR1848028
4. BOHMAN, T. and KRAVITZ, D. (2006). Creating agiantcomponent. Combin. Probab. Comput. 15 489-511. MR2238042
5. BOLLOBÁS, B. (1984). The evolution of randomgraphs. Trans. Amer. Math. Soc. 286 257-274. MR0756039
6. DA COSTA, R. A., DOROGOVTSEV, S. N., GOLTSEV, A. V. and MENDES, J. F. F. (2010). Explosive percolation transition is actually continuous. Phys. Rev. Lett. 105 255701.
7. D' SOUZA, R. M. and MITZENMACHER, M. (2010). Local cluster aggregation models of explosive percolation. Phys. Rev. Lett. 104 195702.
8. ERDÖS, P. and RÉNYI, A. (1960). On the evolution of random graphs. Magyar Tud. Akad. Mat. Kutató Int. Közl. 5 17-61. MR0125031
9. FRIEDMAN, E. J. and LANDSBERG, A. S. (2009). Construction and analysis of random networks with explosive percolation. Phys. Rev. Lett. 103 255701.
10. JANSON, S. and SPENCER, J. (2012). Phase transitions for modified Erdo?s-Rényi processes. Ark. Math. To appear. Available at ar Xiv:1005. 4494.
11. MCDIARMID, C. (1989). On the method of bounded differences. In Surveys in Combinatorics, 1989 (Norwich, 1989). London Mathematical Society Lecture Note Series 141 148-188. Cambridge Univ. Press, Cambridge. MR1036755
12. NAGLER, J., LEVINA, A. and TIMME, M. (2011). Impact of single links in competitive percolation. Nature Physics 7 265-270.
13. RIORDAN, O. and WARNKE, L. (2011). Explosivepercolationis continuous. Science333 322324.
14. SPENCER, J. (2010). Potpourri. J. Comb. 1 237-264. MR2799211
15. SPENCER, J. and WORMALD, N. (2007). Birth control for giants. Combinatorica 27 587-628. MR2375718
16. WORMALD, N. C. (1999). The differential equation method for random graph processes and greedy algorithms. In Lectures on Approximation and Randomized Algorithms 73-155. PWN, Warsaw.