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In order to better understand localization properties in many-body systems, we consider quantum harmonic oscillator lattices with random coefficients. Under certain verifiable conditions on the effective one-particle Hamiltonian, we prove: - a strong form of dynamical localization, expressed in terms of a zero-velocity Lieb-Robinson bound; - exponential decay of static and dynamic correlation functions at both zero and positive temperature; - an area law for the bipartite entanglement of both the ground state and thermal states, as measured by the logarithmic negativity. Our conditions are satisfied for some standard models that are almost surely gapless in the thermodynamic limit. The talk will provide a general overview of these results. This is joint work with Bruno Nachtergaele and Gunter Stolz