A flexible control of wave scattering in complex media is relevance different areas classical and quantum physics. Recently, great interest has been devoted to engineering non-Hermitian systems, with the prediction demonstration new classes potentials unique properties, such as transparent invisible or one-way reflectionless potentials. Such have found for both continuous discrete (lattice) sys...

The present paper extends the landscape theory pioneered in [FM, ADFJM2, DFM] to tight-binding Schr\"odinger operator on $\Z^d$. In particular, we establish upper and lower bounds for integrated density of states terms counting function based upon localization landscape.