Anderson-Bernoulli Localization On 2d And 3d Lattice

The Anderson model describes the behaviour of electrons inside a piece of metal with uniform impurity.The Anderson-Bernoulli model is a special case of the Anderson model where the potential has Bernoulli distribution. We consider Anderson-Bernoulli localization on d dimensional lattice for d=2,3. For d=2, we prove that, if the potential has symmetric Bernoulli distribution and the disorder is large, then localization happens outside a small neighborhood of finitely many energies. For d=3, we prove that localization happens at the bottom of the spectrum.