Random walks, polymers, percolation, and quantum gravity in two dimensions

Physica A: Statistical Mechanics and its Applications

Volumn 263, Issue 1-4, 1999, Pages 452-465

  Duplantier, Bertrand ^a,b  

^a Centre National de la Recherche Scientifique   (France)

^b INSTITUT HENRI POINCARÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040602731     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(98)00638-4     Document Type: Article

References (65)

1. K. Symanzyk, in Local Quantum Theory, edited by R. Jost (Academic, London, New-York, 1969); P.G. de Gennes, Phys. Lett. A38, 339 (1972).
2. K. Symanzyk, in Local Quantum Theory, edited by R. Jost (Academic, London, New-York, 1969); P.G. de Gennes, Phys. Lett. A38, 339 (1972).
3. M. Aizenman, Phys. Rev. Lett. 47, 1 (1981); Commun. Math. Phys. 86, 1 (1982); D.C. Brydges, J. Fröhlich, and T. Spencer, Commun. Math. Phys. 83, 123 (1982).
4. M. Aizenman, Phys. Rev. Lett. 47, 1 (1981); Commun. Math. Phys. 86, 1 (1982); D.C. Brydges, J. Fröhlich, and T. Spencer, Commun. Math. Phys. 83, 123 (1982).
5. M. Aizenman, Phys. Rev. Lett. 47, 1 (1981); Commun. Math. Phys. 86, 1 (1982); D.C. Brydges, J. Fröhlich, and T. Spencer, Commun. Math. Phys. 83, 123 (1982).
6. B. Mandelbrot, The fractal geometry of nature (New-York, Freeman, 1982).
7. G.F. Lawler, Commun. Math. Phys. 86, 539 (1982); Intersection of Random Walks (Boston, Birkhäuser, 1991).
8. G.F. Lawler, Commun. Math. Phys. 86, 539 (1982); Intersection of Random Walks (Boston, Birkhäuser, 1991).
9. M. Aizenman, Commun. Math. Phys. 97, 91 (1985); G. Felder and J. Fröhlich, ibid., 111; G.F. Lawler, ibid., 583.
10. M. Aizenman, Commun. Math. Phys. 97, 91 (1985); G. Felder and J. Fröhlich, ibid., 111; G.F. Lawler, ibid., 583.
11. M. Aizenman, Commun. Math. Phys. 97, 91 (1985); G. Felder and J. Fröhlich, ibid., 111; G.F. Lawler, ibid., 583.
12. B. Duplantier, Commun. Math. Phys. 117, 279 (1987).
13. B. Duplantier and K.-H. Kwon, Phys. Rev. Lett. 61, 2514 (1988).
14. B. Li, and A. D. Sokal, J. Stat. Phys. 61, 723 (1990); E. E. Puckette, and W. Werner, Elect. Comm. in Probab. 1, 5 (1996).
15. B. Li, and A. D. Sokal, J. Stat. Phys. 61, 723 (1990); E. E. Puckette, and W. Werner, Elect. Comm. in Probab. 1, 5 (1996).
16. K. Burdzy and G.F. Lawler, Probab. Th. Rel. Fields 84, 393 (1990); Ann. Probab. 18, 981 (1990).
17. K. Burdzy and G.F. Lawler, Probab. Th. Rel. Fields 84, 393 (1990); Ann. Probab. 18, 981 (1990).
18. B.B Mandelbrot, J. Fluid. Mech. 62, 331 (1974).
19. H.G.E. Hentschel and I. Procaccia, Physica (Amsterdam) 8D, 835 (1983).
20. U. Frisch and G. Parisi, in Proceedings of the International School of Physics "Enrico Fermi", course LXXXVIII, edited by M. Ghil (North-Holland, New York, 1985) p. 84.
21. T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, and B.I. Shraiman, Phys. Rev. A33, 1141 (1986).
22. A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Nucl. Phys. B241, 333 (1984).
23. D. Friedan, J. Qiu, and S. Shenker, Phys. Rev. Lett. 52, 1575 (1984).
24. See, e.g., B. Nienhuis, in Phase transition and critical phenomena, vol. 11, ed. C. Domb and J.L. Lebowitz (Academic, London, 1987).
25. B. Duplantier, Phys. Rev. Lett. 57, 941 (1986); J. Stat. Phys. 54, 581 (1989).
26. B. Duplantier, Phys. Rev. Lett. 57, 941 (1986); J. Stat. Phys. 54, 581 (1989).
27. B. Duplantier and H. Saleur, Phys. Rev. Lett. 57, 3179 (1986); H. Saleur, J. Phys. A19 L807 (1986).
28. B. Duplantier and H. Saleur, Phys. Rev. Lett. 57, 3179 (1986); H. Saleur, J. Phys. A19 L807 (1986).
29. M. Cates and J.M. Deutsch, Phys. Rev. A35, 4907 (1987); B. Duplantier and A. Ludwig, Phys. Rev. Lett. 66, 247 (1991); C. von Ferber, Nucl. Phys. B490, 511 (1997).
30. M. Cates and J.M. Deutsch, Phys. Rev. A35, 4907 (1987); B. Duplantier and A. Ludwig, Phys. Rev. Lett. 66, 247 (1991); C. von Ferber, Nucl. Phys. B490, 511 (1997).
31. M. Cates and J.M. Deutsch, Phys. Rev. A35, 4907 (1987); B. Duplantier and A. Ludwig, Phys. Rev. Lett. 66, 247 (1991); C. von Ferber, Nucl. Phys. B490, 511 (1997).
32. M.E. Cates and T.A. Witten, Phys. Rev. Lett. 56, 2497 (1986); Phys. Rev. A35, 1809 (1987).
33. M.E. Cates and T.A. Witten, Phys. Rev. Lett. 56, 2497 (1986); Phys. Rev. A35, 1809 (1987).
34. R. Langlands, P. Pouliot, and Y. Saint-Aubin, Bull. AMS 30, 1 (1994); J. L. Cardy, J. Phys. A25, L201 (1992).
35. R. Langlands, P. Pouliot, and Y. Saint-Aubin, Bull. AMS 30, 1 (1994); J. L. Cardy, J. Phys. A25, L201 (1992).
36. M. Aizenman, in Mathematics of Multiscale Materials; the IMA Volumes in Mathematics and its Applications, K.M. Golden et al. eds, Springer-Verlag (1998).
37. I. Benjamini, and O. Schramm, Commun. Math. Phys. 197, 75 (1998).
38. B. Duplantier, Saclay preprint SPhT 98/063, Phys. Rev. Lett., in press.
39. B. Duplantier (to be published).
40. A.M. Polyakov, Mod. Phys. Lett. A2, 893 (1987); V.G. Knizhnik, A.M. Polyakov and A.B. Zamolodchikov, Mod. Phys. Lett. A3, 819 (1988).
41. A.M. Polyakov, Mod. Phys. Lett. A2, 893 (1987); V.G. Knizhnik, A.M. Polyakov and A.B. Zamolodchikov, Mod. Phys. Lett. A3, 819 (1988).
42. See, e.g., A.M. Polyakov, Gauge fields and Strings (Harwood-Academic, Chur, 1987).
43. D.V. Boulatov, et al., Nucl. Phys. B275, 641 (1986); F. David, Nucl. Phys. B257, 45, 543 (1985); J. Ambjorn, B. Durhuus, and J. Fröhlich, ibid., 433.
44. D.V. Boulatov, et al., Nucl. Phys. B275, 641 (1986); F. David, Nucl. Phys. B257, 45, 543 (1985); J. Ambjorn, B. Durhuus, and J. Fröhlich, ibid., 433.
45. D.V. Boulatov, et al., Nucl. Phys. B275, 641 (1986); F. David, Nucl. Phys. B257, 45, 543 (1985); J. Ambjorn, B. Durhuus, and J. Fröhlich, ibid., 433.
46. V.A. Kazakov, Phys. Lett. A119, 140 (1986).
47. B. Duplantier and I.K. Kostov, Phys. Rev. Lett. 61, 1436 (1988) ; Nucl. Phys. B 340, 491 (1990).
48. B. Duplantier and I.K. Kostov, Phys. Rev. Lett. 61, 1436 (1988) ; Nucl. Phys. B 340, 491 (1990).
49. See also: F. David, Mod. Phys. Lett. A3, 1651 (1988); J. Distler and H. Kawai, Nucl. Phys. B321 509 (1988).
50. See also: F. David, Mod. Phys. Lett. A3, 1651 (1988); J. Distler and H. Kawai, Nucl. Phys. B321 509 (1988).
51. I.K. Kostov and M.L. Mehta, Phys. Lett. B189, 118 (1987).
52. W. Werner, Probab. Th. Rel. Fields 108, 131 (1997).
53. G.F. Lawler and W. Werner (to be published).
54. G.F. Lawler, Elect. Comm. in Probab. 1 (29) (1996).
55. J.F. Joanny, L. Leibler, and R.C. Ball, J. Chem. Phys. 81, 4640 (1984).
56. C. von Ferber and Y. Holovatch, Europhys. Lett. 39, 31 (1997); Phys. Rev. E 56, 6370 (1997).
57. C. von Ferber and Y. Holovatch, Europhys. Lett. 39, 31 (1997); Phys. Rev. E 56, 6370 (1997).
58. J. Cardy, Nucl. Phys. B240 [FS12], 514 (1984).
59. B.B. Mandelbrot, and C.J.G. Evertsz, Nature 348, 143 (1990).
60. N.G. Makarov, Proc. London Math. Soc. 51, 369 (1985).
61. R.C. Ball and R. Blumenfeld, Phys. Rev. A 44, R828 (1991);
62. B. Duplantier, Saclay preprint SphT 98/125.
63. B. Duplantier, M. Aizenman and A. Aharony, (to be published).
64. H. Saleur and B. Duplantier, Phys. Rev. Lett. 58, 2325 (1987).
65. T. Grossman and A. Aharony, J. Phys. A 20, L1193 (1987).