Let T be an infinite tree in which every vertex α has, independently of the other vertices, a random degree d(α) and every edge has, independently of the other edges, a random conductivity σ. We employ the moment generating function's technique to obtain a formula for the total conductivity of T. We also obtain bounds for the conductivity of spherically symmetric infinite random trees. Assume that every edge of a homogeneous tree T is conducting (open) with probability p or nonconducting (closed) with probability q=1-p. We use the branching processes' argument to reobtain the critical probability. Pc above which percolation occurs; that is, there exists infinite conducting (open) component of T. We also give a sufficient condition for obtaining none such conducting component in case that the probabilities p and q are depending on edge distance from the root of T.
Konsowa, M., Benduilali, B., & Haroon, A. (1991). Conductivity of Random Trees and the Existence of Infinite Conducting Components- Percolation Model. The Egyptian Statistical Journal, 35(2), 251-266. doi: 10.21608/esju.1991.315017
MLA
Mokhtar H. Konsowa; Boualem Benduilali; Ahmed H. Haroon. "Conductivity of Random Trees and the Existence of Infinite Conducting Components- Percolation Model", The Egyptian Statistical Journal, 35, 2, 1991, 251-266. doi: 10.21608/esju.1991.315017
HARVARD
Konsowa, M., Benduilali, B., Haroon, A. (1991). 'Conductivity of Random Trees and the Existence of Infinite Conducting Components- Percolation Model', The Egyptian Statistical Journal, 35(2), pp. 251-266. doi: 10.21608/esju.1991.315017
VANCOUVER
Konsowa, M., Benduilali, B., Haroon, A. Conductivity of Random Trees and the Existence of Infinite Conducting Components- Percolation Model. The Egyptian Statistical Journal, 1991; 35(2): 251-266. doi: 10.21608/esju.1991.315017
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