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Abstract

The resistivity of a one-dimensional lattice consisting of randomly distributed conductivity and insulating sites is considered. Tunneling resistance of the form R[sub o] i e[sup bi] is assumed for a cluster of i adjacent insulating sites. Three different ensembles are considered and compared. In the first ensemble the number of insulating "atoms" is fixed and distributed in a linear chain; in the second one there exists a fixed probability p of having an insulator "atom" occupying a site in a linear chain, and finally the third one consists of a line bent into a circle and the probability p is considered. It is observed that in the thermodynamic limit, the average ensemble resistance per site diverges at the critical filling fraction p[sub c] = e[sup –b], while the variance of the resistance diverges at the lower filling fraction p[sub c1] = p[sup 2/c] . Computer simulations of large but finite systems, however, exhibit a much weaker divergence of the resistance per site at p[sub c] and no divergence of the variance at P[sub c1].