Abstract
We investigate the distribution functionQ(P) describing the survival probability on a comb consisting of a backbone with lateral, randomly disconnected infinite branches. Two different regimes are analyzed in some detail: (i) at short times,Q(P) is shown to have a self-similar structure (devil's staircase); (ii) at large times, this function becomes smooth and tends toward a rather well-defined unit step function. The disorder-averaged survival probability <p 0(t)> is expected to decrease ast −3/4 at large times, whereas the relative fluctuations of the sample-dependentp 0(t) display a very slow decay in time, going to zero liket −1/8.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. H. Weiss and S. Havlin,Phil. Mag. B 56:941 (1987).
S. Havlin, J. E. Kiefer, and G. H. Weiss,Phys. Rev. A 36:1403 (1987).
C. Aslangul, N. Pottier, and P. Chvosta,Physica A 203:533 (1994).
G. H. Weiss and S. Havlin,Physica 13A:474 (1986).
J.-M. Luck,Systèmes désordonnés undimensionnels (Aléa, Saclay, 1992).
R. M. and M. Hervé, Private communication.
A. T. Bharucha-Reid,Elements of the Theory of Markov Processes and Their Applications (McGraw-Hill, New York, 1960).
M. Lavrentiev and B. Chabat,Méthodes de la théorie des fonctions d'une variable complexe (Mir, 1972), Chapter VI.
B. Derrida and E. Gardner,J. Phys. (Paris),45:1283 (1984).
M. Hervé,Les fonctions analytiques (PUF, 1982).
C. M. Bender and S. A. Orszag,Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1984), Chapter VI.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Aslangul, C., Chvosta, P. Diffusion on a random comb: Distribution function of the survival probability. J Stat Phys 78, 1403–1428 (1995). https://doi.org/10.1007/BF02180137
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02180137