  We study the wave function localization properties in a d-dimensional model
of randomly spaced particles with isotropic hopping potential depending solely
on Euclidean interparticle distances. Due to the generality of this model
usually called the Euclidean random matrix model, it arises naturally in
various physical contexts such as studies of vibrational modes, artificial
atomic systems, liquids and glasses, ultracold gases and photon localization
phenomena. We generalize the known Burin-Levitov renormalization group
approach, formulate universal conditions sufficient for localization in such
models and inspect a striking equivalence of the wave function spatial decay
between Euclidean random matrices and translation-invariant long-range lattice
models with a diagonal disorder.
