Localization transition on complex networks via spectral statistics

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 72, Issue 6, 2005, Pages

  Sade, M ^a   Kalisky, T ^a   Havlin, S ^a   Berkovits, R ^a  

^a BAR ILAN UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

METAL INSULATOR BOUNDARIES; STATISTICAL METHODS;

COMPACT STRUCTURE; COMPLEX NETWORKS; CONNECTIVITY; SPECTRAL STATISTICS;

PHASE TRANSITIONS;

EID: 33244473946     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.066123     Document Type: Article

References (43)

1. P. W. Anderson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.109.1492 109, 1492 (1958);
2. D. J. Thouless, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(74)90029-5 13, 93 (1974).
3. See these reviews and references within G. Bergmann, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(84)90103-0 107, 1 (1984);
4. P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.57.287 57, 287 (1985);
5. R. Berkovits and S. Feng, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(94)90079-5 238, 135 (1994);
6. M. C. W. van Rossum and T. M. Nieuwenhuizen, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.71.313 71, 313 (1999).
7. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.42.673 42, 673 (1979).
8. C. Castellani, C. DiCastro, and L. Peliti, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/19/17/009 19, L1099 (1986);
9. H. Kunz and B. Souillard, J. Plasma Phys. JPLPBZ 0022-3778 44, L503 (1983);
10. J. P. Straley, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.28.5393 28, 5393 (1983);
11. T. Lukes, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/12/20/006 12, L797 (1979);
12. K. B. Efetov, Sov. Phys. JETP SPHJAR 0038-5646 61, 606 (1985).
13. A. D. Mirlin and Y. V. Fyodorov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.526 72, 526 (1994).
14. B. Kramer and A. MacKinnon, Rep. Prog. Phys. RPPHAG 0034-4885 56, 1496 (1993).
15. K. Slevin, T. Ohtsuki, and T. Kawarabayashi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.3915 84, 3915 (2000).
16. I. K. Zharekeshev and B. Kramer, Ann. Phys. ANPYA2 0003-3804 10.1002/(SICI)1521-3889(199811)7:5/6<442::AID-ANDP442>3.3.CO;2-4 7, 442 (1998).
17. M. Schreiber and H. Grussbach, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1687 76, 1687 (1996).
18. R. Albert, H. Jeong, and A. L. BarabÃsi, Nature (London) NATUAS 0028-0836 406, 6794 (2000).
19. For a recent review see R. Albert and A. L. BarabÃsi, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.47 74, 47 (2002).
20. S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks-From Biological Nets to the Internet and WWW (Oxford University Press, Oxford, 2003).
21. R. Pastor-Satorras and A. Vespignani, Evolution and Structure of the Internet: A Statistical Physics Approach (Cambridge University Press, Cambridge, 2004).
22. R. Cohen, K. Erez, D. Ben-Avraham, and S. Havlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.4626 85, 4626 (2000);
23. R. Cohen, K. Erez, D. Ben-Avraham, and S. Havlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.3682 86, 3682 (2001).
24. R. Cohen and S. Havlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.058701 90, 058701 (2003).
25. B. Bollobas and O. Riordan in Handboook of graphs and networks, edited by, S. Bornholdt, and, H. G. Schuster, (Wiley-VCH, Berlin, 2002).
26. M. Molloy and B. Reed, Combinatorics, Probab. Comput. CPCOFG 0963-5483 10.1017/S0963548398003526 7, 295 (1998).
27. D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.5468 85, 5468 (2000).
28. M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 64, 026118 (2001).
29. C. P. Zhu and S.-J. Xiong, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.14780 62, 14780 (2000).
30. O. Giraud, B. Georgeot, and D. L. Shepelyansky, quant-ph/0503188.
31. M. Sade and R. Berkovits, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.193102 68, 193102 (2003).
32. Y. V. Fyodorov and A. D. Mirlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.2049 67, 2049 (1991);
33. S. N. Evangelou and E. N. Economou, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.361 68, 361 (1992);
34. Y. V. Fyodorov, J. Phys. I JPGCE8 1155-4304 10.1051/jp1:1992229 2, 1571 (1992);
35. Y. V. Fyodorov and A. D. Mirlin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.55.R16001 55, R16001 (1997).
36. L. A. Braunstein, S. V. Buldyrev, R. Cohen, S. Havlin, and H. E. Stanley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.168701 91, 168701 (2003).
37. E. Lopez, S. V. Buldyrev, S. Havlin, and H. E. Stanley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.248701 94, 248701 (2005).
38. E. M. Bollt and D. Ben-Avraham, cond-mat/0409465.
39. B. Shapiro, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.48.823 48, 823 (1982).
40. P. ErdÃs and A. RÃnyi, Publ. Math. (Debrecen) PUMAAR 0033-3883 6, 290 (1959).
41. T. Kalisky, R. Cohen, D. Ben-Avraham, and S. Havlin, in Lecture Notes in Physics: Proceedings of the 23rd LANL-CNLS Conference, “ Complex Networks, Santa-Fe, 2003, edited by, E. Ben-Naim, H. Frauenfelder, and, Z. Toroczkai, (Springer, Berlin, 2004).
42. B. I. Shklovskii, B. Shapiro, B. R. Sears, P. Lambrianides, and H. B. Shore, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.47.11487 47, 11487 (1993).
43. R. Berkovits and Y. Avishai, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.53.R16125 53, R16125 (1996).