Rigorous confidence intervals for critical probabilities

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

Volumn 76, Issue 1, 2007, Pages

  Riordan, Oliver ^a   Walters, Mark ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CHEMICAL BONDS; COMPUTATIONAL METHODS; CRYSTAL LATTICES; PROBABILITY;

ARCHIMEDEAN LATTICES; BOND PERCOLATION; CONFIDENCE INTERVALS; CRITICAL PROBABILITIES;

PERCOLATION (SOLID STATE);

EID: 34547150499     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.011110     Document Type: Article

References (46)

1. B. Grünbaum and G. C. Shephard, Tilings and Patterns (W. H. Freeman, New York, 1987), pp. xii+700.
2. G. Grimmett, Percolation, 2nd ed. (Springer, New York, 1999), pp. xiv+444.
3. B. Bollobás and O. Riordan, Percolation (Cambridge University Press, Cambridge, UK, 2006).
4. H. Kesten, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01197577 74, 41 (1980).
5. H. Kesten, Percolation Theory for Mathematicians (Birkhäuser, Boston, 1982), pp. iv+423.
6. J. C. Wierman, Adv. Appl. Probab. AAPBBD 0001-8678 10.2307/1426685 13, 298 (1981).
7. M. F. Sykes and J. W. Essam, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.10.3 10, 3 (1963).
8. M. F. Sykes and J. W. Essam, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704215 5, 1117 (1964).
9. J. C. Wierman, in Disorder in Physical Systems: A Volume in Honour of John Hammersley, edited by, G. R. Grimmett, and, D. J. A. Welsh, (Oxford University Press, New York, 1990), pp. 349-360.
10. J. C. Wierman, Combinatorics, Probab. Comput. CPCOFG 0963-5483 10.1017/S0963548302005370 12, 95 (2003).
11. J. C. Wierman, Random Struct. Algorithms RSALFD 1042-9832 10.1002/RSA.10029 20, 507 (2002).
12. R. Parviainen and J. C. Wierman, see, e.g. http://citeseer.ist.psu.edu/ 577889.html.
13. W. D. May and J. C. Wierman, Combinatorics, Probab. Comput. CPCOFG 0963-5483 10.1017/S0963548305006802 14, 549 (2005).
14. P. J. Reynolds, H. E. Stanley, and W. Klein, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.21.1223 21, 1223 (1980).
15. R. M. Ziff and B. Sapoval, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/19/18/010 19, 1169 (1986).
16. F. Yonezawa, S. Sakamoto, and M. Hori, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.636 40, 636 (1989).
17. P. N. Suding and R. M. Ziff, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.275 60, 275 (1999).
18. M. E. J. Newman and R. M. Ziff, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.016706 64, 016706 (2001).
19. M. E. J. Newman and R. M. Ziff, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.4104 85, 4104 (2000).
20. R. Parviainen, " Estimation of bond percolation thresholds on the Arhimedean lattices, " report available from http://www.ms.unimelb.edu.au/ ~robertp/ (2005).
21. R. M. Ziff and M. E. J. Newman, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.016129 66, 016129 (2002).
22. B. Bollobás and A. Stacey, J. Appl. Probab. JPRBAM 0021-9002 10.2307/3215002 34, 859 (1997).
23. P. Balister, B. Bollobás, and M. Walters, Random Struct. Algorithms RSALFD 1042-9832 10.1002/rsa.20064 26, 392 (2005).
24. B. Bollobás and O. Riordan, Bull. London Math. Soc. LMSBBT 0024-6093 10.1112/S002460930601842X 38, 470 (2006).
25. T. M. Liggett, R. H. Schonmann, and A. M. Stacey, Ann. Probab. APBYAE 0091-1798 10.1214/aop/1024404279 25, 71 (1997).
26. M. V. Menshikov, Dokl. Akad. Nauk SSSR DANKAS 0002-3264 288, 1308 (1986).
27. B. Bollobás and O. Riordan, eprint arXiv:math.PR/0606149.
28. S. Sheffield, Asterisque ZZZZZZ 0303-1179 304, (2003).
29. M. Matsumoto and T. Nishimura, ACM Trans. Model. Comput. Simul. ATMCEZ 1049-3301 10.1145/272991.272995 8, 3 (1998).
30. http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html.
31. R. Langlands, P. Pouliot, and Y. Saint-Aubin, Bull., New Ser., Am. Math. Soc. ZZZZZZ 0273-0979 30, 1 (1994).
32. J. L. Cardy, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/25/4/009 25, L201 (1992).
33. S. Smirnov and W. Werner, Math. Res. Lett. ZZZZZZ 1073-2780 8, 729 (2001).
34. O. Schramm, Isr. J. Math. ISJMAP 0021-2172 118, 221 (2000).
35. G. F. Lawler, O. Schramm, and W. Werner, Acta Math. ACMAA8 0001-5962 10.1007/BF02392618 187, 237 (2001).
36. G. F. Lawler, O. Schramm, and W. Werner, Acta Math. ACMAA8 0001-5962 10.1007/BF02392619 187, 275 (2001).
37. G. F. Lawler, O. Schramm, and W. Werner, Electron. J. Probab. ZZZZZZ 1083-6489 7, 13 (2002).
38. G. F. Lawler, O. Schramm, and W. Werner, Ann. I.H.P. Probab. Stat. ZZZZZZ 0246-0203 38, 109 (2002).
39. S. Smirnov, C. R. Acad. Sci., Ser. I: Math. CASMEI 0764-4442 10.1016/S0764-4442(01)01991-7 333, 239 (2001).
40. http://www.dpmms.cam.ac.uk/~walters/lattice_bounds/.
41. R. M. Ziff, P. T. Cummings, and G. Stell, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/17/15/018 17, 3009 (1984).
42. R. M. Ziff, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.016134 73, 016134 (2006).
43. F. Y. Wu, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/12/17/002 12, L645 (1979).
44. C. Tsallis, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/15/23/007 15, L757 (1982).
45. R. M. Ziff and P. N. Suding, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/30/15/021 30, 5351 (1997).
46. C. R. Scullard and R. M. Ziff, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.045102 73, 045102 (R) (2006).