Conductivity of Random Trees and the Existence of Infinite Conducting Components- Percolation Model | ||
| The Egyptian Statistical Journal | ||
| Article 5, Volume 35, Issue 2, December 1991, Pages 251-266 | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.1991.315017 | ||
| Authors | ||
| Mokhtar H. Konsowa; Boualem Benduilali; Ahmed H. Haroon | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| Conductivity; Random trees; Percolation; Branching Processes; Extinction Probability | ||
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