Lévy-flight spreading of epidemic processes leading to percolating clusters

European Physical Journal B

Volumn 7, Issue 1, 1999, Pages 137-145

  Janssen, H K ^a   Oerding, K ^a   Van Wijland, F ^b   Hilhorst, H J ^b  

^a HEINRICH HEINE UNIVERSITY   (Germany)

^b UNIVERSITÉ PARIS SUD   (France)

Author keywords

05.40.+j Fluctuation phenomena, random processes, and Brownian motion; 64.60.Ak Renormalization group, fractal, and percolation studies of phase transitions; 64.60.Ht Dynamic critical phenomena

Indexed keywords

EID: 0000371614     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100510050596     Document Type: Article

References (49)

1. P. Grassberger, K. Sundermeyer, Phys. Lett. B 77, 220 (1978).
2. P. Grassberger, A. de la Torre, Ann. Phys. (New York) 122, 373 (1979).
3. V.N. Gribov, Zh. Eksp. Teor. Fiz. 53, 654 (1967); Sov. Phys. JETP 26, 414 (1968).
4. V.N. Gribov, Zh. Eksp. Teor. Fiz. 53, 654 (1967); Sov. Phys. JETP 26, 414 (1968).
5. V.N. Gribov, A.A. Migdal, Zh. Eksp. Teor. Fiz. 55, 1498 (1968); Sov. Phys. JETP 28, 784 (1969).
6. V.N. Gribov, A.A. Migdal, Zh. Eksp. Teor. Fiz. 55, 1498 (1968); Sov. Phys. JETP 28, 784 (1969).
7. M. Moshe, Phys. Rep. C 37, 255 (1978).
8. H.K. Janssen, Z. Phys. B: Cond. Mat. 42, 151 (1981).
9. F. Schlögl, Z. Phys. 225, 147 (1972).
10. D. Mollison, J. R. Stat. Soc. B 39, 283 (1977).
11. N.T.J. Bailey, The Mathematical Theory of Infectious Diseases (Griffin, London, 1975).
12. J.D. Murray, Mathematical Biology (Springer, Berlin, 1989).
13. S.R. Broadbent, J.M. Hammersley, Proc. Camb. Philos. Soc. 53, 629 (1957).
14. J.L. Cardy, R.L. Sugar, J. Phys. A: Math. Gen. 13, L423 (1980).
15. S.P. Obukhov, Physica A 101, 145 (1980).
16. A. Bunde, S. Havlin, in Fractals and Disordered Systems, 2nd edn., edited by A. Bunde, S. Havlin (Springer, Berlin, 1996).
17. P. Grassberger, Math. Biosci. 62, 157 (1983).
18. H.K. Janssen, Z. Phys. B: Cond. Mat. 58, 311 (1985).
19. J.L. Cardy, P. Grassberger, J. Phys. A: Math. Gen. 18, L267 (1985).
20. P. Grassberger, Z. Phys. B: Cond. Mat. 47, 365 (1982).
21. T.E. Harris, Ann. Prob. 2, 969 (1974).
22. T.M. Liggett, Interacting Particle Systems (Springer, New York, 1985).
23. I. Jensen, R. Dickman, Physica A 203, 175 (1994).
24. W. Kinzel, in Percolation Structures and Processes, edited by G. Deutsch, R. Zallen, J. Adler (Hilger, Bristol, 1983).
25. W. Kinzel, Z. Phys. B: Cond. Mat. 58, 229 (1985).
26. P. Grassberger, in Fractals in physics, edited by L. Pietronero, E. Tosatti (Elsevier, 1986).
27. E.W. Montroll, B.J. West, Fluctuation Phenomena, edited by E.W. Montroll, J.L. Lebowitzl (North-Holland, Amsterdam, 1979).
28. S. Bochner, Lectures on Fourier Integrals (University Press, Princeton, 1959).
29. H.K. Janssen, Phys. Rev. E 58, R2673 (1998).
30. G. Zumofen, J. Klafter, Phys. Rev. E 50, 5119 (1994).
31. K. Oerding, J. Phys. A: Math. Gen. 29, 7051 (1996).
32. M.W. Deem, J.-M. Park, Phys. Rev. E 57, 2681 (1998); ibid. 3618.
33. M.W. Deem, J.-M. Park, Phys. Rev. E 57, 2681 (1998); ibid. 3618.
34. H.K. Janssen, Z. Phys. B: Cond. Mat. 23, 377 (1976).
35. C. De Dominicis, J. Phys. France Colloq. 37, C247 (1976).
36. H.K. Janssen, in From Phase Transitions to Chaos, edited by G. Györgyi, I. Kondor, L. Sasvári, T. Tél (Worl Scientific, Singapore, 1992).
37. P.C. Martin, E.D. Siggia, H.A. Rose, Phys. Rev. A 8, 423 (1973).
38. M. Doi, J. Phys. A: Math. Gen. 9, 1479 (1976).
39. P. Grassberger, M. Scheunert, Forstschr. Phys. 28, 547 (1980).
40. L. Peliti, J. Phys. France 46, 1469 (1985).
41. F. van Wijland, K. Oerding, H.J. Hilhorst, Physica A 251, 179 (1998).
42. H.K. Janssen, B. Schaub, B. Schmittmann, Z. Phys. B: Cond. Mat. 73, 539 (1989).
43. E.V. Albano, Europhys. Lett. 34, 97 (1996).
44. J.L. Cardy, U.C. Täuber, Phys. Rev. Lett. 77, 4780 (1996).
45. J.L. Cardy, U.C. Täuber, J. Stat. Phys. 90, 1 (1998).
46. R.G. Priest, T.C. Lubensky, Phys. Rev. B 13, 4159 (1976).
47. D.J. Amit, J. Phys. A: Math. Gen. 9, 1441 (1976).
48. A. Aharony, in Phase transitions and critical phenomena, Vol. 6, edited by C. Domb, M.S. Green (New York: Academic, 1976), p. 357.
49. S. Prakash, S. Havlin, M. Schwartz, H.E. Stanley, Phys. Rev. A 46, R1724 (1992).