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Abstract : |
Abstract. This paper contains the proofs of Theorems 2 and 3 of the article entitled Random electrical networks on complete graphs, written by the same authors and published in the Journal of the London Mathematical Society, vol. 30 (1984), pp. 171--192. The current paper was written in 1983 but was not published in a journal, although its existence was announced in the LMS paper. This T E X version was created on 9 July 2001. It incorporates minor improvements to formatting and punctuation, but no change has been made to the mathematics. We study the e#ective electrical resistance of the complete graph Kn+2 when each edge is allocated a random resistance. These resistances are assumed independent with distribution P(R =, |
