Abstract
The resistance of a random one-dimensional chain is calculated in a novel way. The electronic wave function is represented by a random walk on a hyperboloid, for which the hyperbolic angle $\ensuremath{\chi}$ is an additive scaling parameter. The resistance is $(\frac{\ensuremath{\pi}\ensuremath{\hbar}}{{e}^{2}}){sinh}^{2}(\frac{\ensuremath{\chi}}{2})$. For strong disorder, $\ensuremath{\chi}$ is normally distributed and explicit expressions can be obtained for the localization length and its variance, in good agreement with the results of various computer experiments.
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