Expected number of distinct sites visited by N Lévy flights on a one-dimensional lattice

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 53, Issue 6, 1996, Pages 5774-5778

  Berkolaiko, G ^a,b,c,d   Havlin, S ^a,b,c,d   Larralde, H ^a,b,c,d   Weiss, G H ^a,b,c,d  

^a VORONEZH STATE UNIVERSITY   (Russian Federation)

^b BAR ILAN UNIVERSITY   (Israel)

^c UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^d NATIONAL INSTITUTES OF HEALTH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000240454     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.53.5774     Document Type: Article

References (34)

1. A. Dvoretzky and P. Erdös, in Proceedings of the Second Berkeley Symposium (University of California Press, Berkeley, 1951), p. 33.
2. G H. Vineyard, J. Math. Phys.4, 1191 (1963).
3. J R. Beeler and J A. Delaney, Phys. Rev.130, 960 (1963).
4. J R. Beeler, Phys. Rev.134, 1396 (1964).
5. H B. Rosenstock, Phys. Rev.187, 1166 (1969).
6. S. Alexander, J. Bernasconi and R. Orbach, Phys. Rev. B17, 4311 (1978).
7. G. Zumofen and A. Blumen, Chem. Phys. Lett.81, 372 (1981);
8. G. Zumofen and A. Blumen, Chem. Phys. Lett.88, 63 (1982).
9. G H. Weiss and S. Havlin, J. Stat. Phys.37, 17 (1984).
10. R F. Kayser and J B. Hubbard, Phys. Rev. Lett.51, 79 (1983);
11. R F. Kayser and J B. Hubbard, J. Chem. Phys.80, 1127 (1984).
12. A. Blumen, J. Klafter, and G. Zumofen, in Optical Spectroscopy of Glasses, edited by I. Zschokke (Reide, New York, 1986).
13. J W. Haus and K W. Kehr, Phys. Rep.150, 263 (1987).
14. F. den Hollander and G. H. Weiss, in Contemporary Problems in Statistical Physics, edited by G. H. Weiss (SIAM, Philadelphia, 1994), p. 147.
15. M v. Smoluchowski, Z. Phys. Chem.29, 129 (1917).
16. S A. Rice, Diffusion-Controlled Reactions (Elsevier, Amsterdam, 1985).
17. E W. Montroll, in Stochastic Processes in Applied Mathematics XVI (American Mathematical Society, Providence, 1964), p. 193.
18. E W. Montroll and G H. Weiss, J. Math. Phys.6, 167 (1965).
19. H. Larralde and G H. Weiss, J. Phys. A28, 5217 (1995).
20. N C. Jain and S. Orey, Isr. J. Math.6, 373 (1968).
21. N C. Jain and W E. Pruitt, in Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley, 1971), Vol. III, p. 31;
22. J. Anal. Math. 27, 94 (1974).
23. H. Larralde, P. Trunfio, S. Havlin, H E. Stanley and G H. Weiss, Nature355, 423 (1992);
24. H. Larralde, P. Trunfio, S. Havlin, H E. Stanley and G H. Weiss, Phys. Rev. A45, 7128 (1992).
25. P. Lévy, Theorie de l'addition des Variables Aleatores (Gauthier-Villars, Paris, 1937).
26. M F. Shlesinger, Annu. Rev. Phys. Chem.39, 269 (1988).
27. J. Klafter, G. Zumofen and A. Blumen, Chem. Phys.177, 821 (1993).
28. G. Zumofen and J. Klafter, Chem. Phys. Lett.219, 303 (1994).
29. M F. Shlesinger, G. Zaslavsky and J. Klafter, Nature263, 31 (1993).
30. B V. Gnedenko and A N. Kolmogoroff, Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, Cambridge, 1954).
31. J E. Gillis and G H. Weiss, J. Math. Phys.11, 4 (1970).
32. G H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
33. A. Blumen, G. Zumofen and J. Klafter, Phys. Rev. A40, 3964 (1989).
34. B D. Hughes, Random Walks and Random Environments (Oxford University Press, Oxford, 1995), Vol. 1.