Dynamical localization for polynomial long-range hopping random operators on $mathbb{Z}^d$

In this paper, we prove a power-law version dynamical localization for a random operator $mathrm{H}_{omega}$ on $mathbb{Z}^d$ with long-range hopping. In breif, for the linear Schrodinger equation $$mathrm{i}partial_{t}u=mathrm{H}_{omega}u, quad u in ell^2(mathbb{Z}^d), $$ the Sobolev norm of the solution with well localized initial state is bounded for any $tgeq 0$.