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Breakage and restoration in recursive trees

Part of: Combinatorial probability Graph theory

Published online by Cambridge University Press:  14 July 2016

Guillermo Tomás Tetzlaff
Guillermo Tomás Tetzlaff*
Affiliation:
Universidad de Buenos Aires and Universidad Nacional de La Plata
*
∗ Postal address: Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Pabelló I, Ciudad Universitaria, (1428) Buenos Aires, Argentina. Email address: tetzlaff@dc.uba.ar
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Abstract

Uniform sequential tree-building aggregation of n particles is analyzed together with the effect of the avalanche that takes place when a subtree rooted at a uniformly chosen vertex is removed. For large n, the expected subtree size is found to be ≃ logn both for the tree of size n and the tree that remains after an avalanche. Repeated breakage-restoration cycles are seen to give independent avalanches which attain size k(1 ≤ k ≤ n-1) with probability (k(k+1))-1 and restored trees that are recursive.

Keywords

Aggregationrecursive treeavalancheself-organized criticality

MSC classification

Primary: 60C05: Combinatorial probability 05C80: Random graphs

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 383 - 390
Copyright
Copyright © Applied Probability Trust 2002 

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References

[1] Bak, P., and Chen, K. (1991). Self-organized criticality. Sci. Amer. 264, 26–33.CrossRefGoogle Scholar
[2] Bak, P., and Sneppen, K. (1993). Punctuated equilibrium and criticality in a simple model of evolution. Phys. Rev. Lett. 71, 4083–4086.Google Scholar
[3] Bergeron, F., Flajolet, P., and Salvy, B. (1992). Varieties of increasing trees. In Proc. 17th Coll. Trees in Algebra and Programming (Lecture Notes Comput. Sci. 581), ed. Raoult, J.-C., Springer, Berlin, pp. 24–48.Google Scholar
[4] Botet, R., and Jullien, R. (1985). Diffusion-limited aggregation with disaggregation. Phys. Rev. Lett. 55, 1943–1946.CrossRefGoogle ScholarPubMed
[5] Eden, M. (1961). A two-dimensional growth process. In Proc. 4th Berkeley Symp. Math. Statist. Prob., Vol. 4, ed. Neyman, F., University of California Press, Berkeley, pp. 223–239.Google Scholar
[6] Family, F., Meakin, P., and Deutch, J. M. (1986). Kinetics of coagulation with fragmentation: scaling behavior and fluctuations. Phys. Rev. Lett. 55, 1943–1946.Google Scholar
[7] Gastwirth, J. L., and Bhattacharya, P. K. (1984). Two probability models of pyramid or chain letter schemes demonstrating that their promotional claims are unreliable. Operat. Res. 32, 527–536.CrossRefGoogle Scholar
[8] Held, G. A., Solina, H., Keane, D. T., Haag, W. J., Horn, P. M., and Grinstein, G. (1990). Experimental study of critical-mass fluctuations in an evolving sandpile. Phys. Rev. Lett. 65, 1120–1123.Google Scholar
[9] Mahmoud, H. M. (1992). Distances in random plane-oriented recursive trees. J. Comput. Appl. Math. 41, 237–245.Google Scholar
[10] Meir, A., and Moon, J. W. (1978). On the altitude of nodes in random trees. Canad. J. Math. 30, 997–1015 Google Scholar
[11] Najock, D., and Heyde, C. C. (1982). On the number of terminal vertices in certain random trees with an application to stemma construction in philology. J. Appl. Prob. 19, 675–680.Google Scholar
[12] Vicsek, T. (1989). Fractal Growth Phenomena. World Scientific, Teaneck, NJ.Google Scholar
[13] Witten, T. A., and Sander, L. M. (1981). Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 47, 1400–1403.Google Scholar