Multiplicity bound of singular spectrum for higher rank Anderson models

In this work, we prove a bound on the multiplicity of the singular spectrum for a certain class of Anderson Hamiltonians. The operator in consideration is the form Hω=Δ+∑n∈ZdωnPn on the Hilbert space ℓ2(Zd), where Δ is discrete laplacian, Pn are projection onto ℓ2({x∈Zd:nili