Asymptotic analysis for the number of subgraphs of a given size in temporal random graphs
DOI:
https://doi.org/10.22199/S07160917.1993.0001.00001Keywords:
Functional central limit theorem, random graphs, differential equationsAbstract
In this work we study a law of large numbers and a functional central limit theorem for the number os subgraphs of given size in a random graph which evolves with the lime. Our motivation comes from the study of reliability measures in communications networks.
References
[1] Ikeda, N.; Watanabe, S.: Stochastic Differential Equations and Diffusion Processes. North-Holland, 1981.
[2] Karonski, M.; Rucinski, A.: Poisson Convergence and Semi-induced Properties of Random Graphs. Math. Proc. Camb. Phil. Soc. 101-291, 1987.
[3] Liggett, T.: Interacting Particle Systems. Springer- Verlag. 1985.
[4] Rebolledo, R.: La Méthode des Martingales Apliquée a l'étude de la Convergence en Loi de Precessus. Bull. Soc. Math. France. Mémoire 62 1-125. 1979.
[5] Rebolledo, R.: Central Limit Theorems for Local Martingales. Z. für W. 51 269-286. 1980.
[6] Rucinski, A.: When Are Small Subgraphs of a Random Graphs Normally Distributed?. Prob. Th. Rel. Fields. 78 1-10. 1988.
[7] Siegrist, K.; Amin, A.; Slater, P.: The Central Limit Theorem and the Law of Large Numbers for pair-connectivity in Bernouilli trees. Prob. Eng. lnor. Sc. 3 477-491. 1989.
[2] Karonski, M.; Rucinski, A.: Poisson Convergence and Semi-induced Properties of Random Graphs. Math. Proc. Camb. Phil. Soc. 101-291, 1987.
[3] Liggett, T.: Interacting Particle Systems. Springer- Verlag. 1985.
[4] Rebolledo, R.: La Méthode des Martingales Apliquée a l'étude de la Convergence en Loi de Precessus. Bull. Soc. Math. France. Mémoire 62 1-125. 1979.
[5] Rebolledo, R.: Central Limit Theorems for Local Martingales. Z. für W. 51 269-286. 1980.
[6] Rucinski, A.: When Are Small Subgraphs of a Random Graphs Normally Distributed?. Prob. Th. Rel. Fields. 78 1-10. 1988.
[7] Siegrist, K.; Amin, A.; Slater, P.: The Central Limit Theorem and the Law of Large Numbers for pair-connectivity in Bernouilli trees. Prob. Eng. lnor. Sc. 3 477-491. 1989.
Published
2018-04-03
How to Cite
[1]
R. Fierro and G. Figueroa, “Asymptotic analysis for the number of subgraphs of a given size in temporal random graphs”, Proyecciones (Antofagasta, On line), vol. 12, no. 1, pp. 1-11, Apr. 2018.
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