An important role in our proof is played by a variant of Stollmann's eigenvalue concentration bound (cf. [St00]). This result, as was proved earlier in [C08], admits a straightforward extension covering the case of multi-particle systems with correlated external random potentials: a subject of our future work. We also stress that the scheme of our proof is not specific to lattice systems, since our main method, the MSA, admits a continuous version. A proof of multi-particle Anderson localization in continuous interacting systems with various types of external random potentials will be published in a separate papers.

We establish the phenomenon of Anderson localisation for a quantum two-particle system on a lattice Z d with short-range interaction and in presence of an IID external potential with sufficiently regular marginal distribution.

We consider a quantum two-particle system on a lattice Z d with interaction and in presence of an IID external potential. We establish Wegner-typer estimates for such a model. The main tool used is Stollmann's lemma.

Let V(θ) be a smooth, non-constant function on the torus and let T be a hyperbolic toral automorphism. Consider a discrete one dimensional Schrόdinger operator H, whose potential at site j is given by gVj -gV(T J θ). We prove that when g ^ 0 is small and g 1 ^2 ^ \E\ ^ 2g 1 ^2, the Lyapunov exponent for the cocycle generated by H-E is proportional to g 2 . The proof relies on a formula of Pastur and Figotin and on symbolic dynamics.

Abstract. We establish lower-edge spectral and dynamical localization for a multiparticle Anderson model in a Euclidean space R d , d ≥ 1, in presence of a non-trivial short-range interaction and an alloy-type random external potential.

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We consider a class of ensembles of lattice Schrödinger operators with deterministic random potentials, including quasi-periodic potentials with Diophantine frequencies, depending upon an infinite number of parameters in an auxiliary measurable space. Using a variant of the Multi-Scale Analysis, we prove Anderson localization for generic ensembles in the strong disorder regime and establish an analog of Minami-type bounds for spectral spacings.

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