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Geometrical disorder is present in many physical situations giving rise toeigenvalue problems. The simplest case of diffusion on a random lattice withfluctuating site connectivities is studied analytically and by exact numericaldiagonalizations. Localization of eigenmodes is shown to be induced bygeometrical defects, that is sites with abnormally low or large connectivities.We expose a ``single defect approximation'' (SDA) scheme founded on thismechanism that provides an accurate quantitative description of both extendedand localized regions of the spectrum. We then present a systematicdiagrammatic expansion allowing to use SDA for finite-dimensional problems,e.g. to determine the localized harmonic modes of amorphous media.Comment: final version as published, 6 pages, 1 ps-figur

A single defect approximation for localized states on random lattices