Multi-type directed scale-free percolation

Communications in Theoretical Physics

Volumn 57, Issue 4, 2012, Pages 701-716

  Shang, Yi Lun ^a  

^a UNIVERSITY OF TEXAS AT SAN ANTONIO   (United States)

Author keywords

chemical distance; directed percolation; long range percolation; phase transition; random graph; regularly varying

Indexed keywords

EID: 84860457020     PISSN: 02536102     EISSN: None     Source Type: Journal    
DOI: 10.1088/0253-6102/57/4/26     Document Type: Article

References (32)

1. R. Albert and A.L. Barabási 2002 Rev. Mod. Phys. 74 47
2. S.N. Dorogovtsev and J.F.F. Mendes 2003 Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, New York)
3. M.E.J. Newman 2010 Networks: An Introduction (Oxford University Press, New York)
4. B. Bollobás, O. Riordan 2003 Mathematical Results on Scale-Free Random Graphs, in: Handbook of Graphs and Networks (Wiley-VCH, Weinheim) p 1-34
5. Y. Shang 2011 EPL 95 28005
6. M. Biskup 2004 Ann. Probab. 32 2933
7. D. Coppersmith, D. Gamarnik and M. Sviridenko 2002 The Diameter of a Long Range Percolation Graph Proc. the 13th Ann. ACM-SIAM Symp. on Discrete Algorithms vol 21 p 1-13
8. C.M. Newman and L.S. Schulman 1986 Comm. Math. Phys. 104 547
9. L.S. Schulman 1983 J. Phys. A 16 L639
10. Y. Shang 2011 Proc. World Acad. Sci. Eng. Tech. 80 1437
11. P. Trapman 2010 Ann. Probab. 38 1583
12. S. Bhamidi and R. van der Hofstad 2010 J. van Leeuwaarden, Elect. J. Probab. 15 1682
13. B. Bollobás, O. Riordan and S. Janson 2007 Rand. Struct. Alg. 31 3
14. T. Britton, M. Deijfen and A. Martin-Löf 2006 J. Stat. Phys. 124 1377 (Pubitemid 44581233)
15. M. Deijfen and W. Kets 2009 Probab. Engrg. Inform. Sci. 23 661
16. I. Norros and H. Reittu 2006 Adv. Appl. Probab. 38 59
17. Y. Shang 2010 Electron. J. Combin. 17 R23
18. P. Erdös and A. Rényi 1959 Publ. Math. Debrecen 6 290
19. M. Deijfen, R. van der Hofstad and G. Hooghiemstra 2011 arXiv:1103.0208
20. N.H. Bingham, C.M. Goldie and J.L. Teugels 1987 Regular Variation (Cambridge University Press, Cambridge)
21. M. Boguñá and M Ángeles Serrano 2005 Phys. Rev. E 72 016106 (Pubitemid 41521093)
22. Y. Shang 2010 Int. Electron. J. Pure Appl. Math. 2 69
23. Y. Shang 2010 Chin. Phys. B 19 070201
24. D.M. Boyd and N.B. Ellison 2007 J. Comput.-Mediated Commun. 13 210
25. T. Kelsey 2010 Social Networking Spaces: From Facebook to Twitter and Everything in Between (Springer-Verlag, New York)
26. H.F. Tipton and M. Krause 2008 Information Security Management Handbook (Auerbach Publications)
27. W. Feller 1971 An Introduction to Probability Theory and its Applications (John Wiley & Sons, New York)
28. T.M. Liggett, R.H. Schonmann and A.M. Stacey 1997 Ann. Probab. 25 71
29. J.E. Yukich 2006 J. Appl. Prob. 43 665
30. B. Bollobás and O. Riordan 2006 Percolation (Cambridge University Press, New York)
31. G. Grimmett 1999 Percolation (Springer, Berlin)
32. A. Gandolfi, M.S. Keane and C.M. Newman 1992 Probab. Th. Rel. Fields. 92 511