  Within the framework of holography applied to condensed matter physics, we
study a model of perturbatively charged disorder in D=4 dimensions. Starting
from initially uncharged AdS_4, a randomly fluctuating boundary chemical
potential is introduced by turning on a bulk gauge field parameterized by a
disorder strength and a characteristic scale k_0. Accounting for gravitational
backreaction, we construct an asymptotically AdS solution perturbatively in the
disorder strength. The disorder averaged geometry displays unphysical
divergences in the deep interior. We explain how to remove these divergences
and arrive at a well behaved solution. The disorder averaged DC conductivity is
calculated and is found to contain a correction to the AdS result. The
correction appears at second order in the disorder strength and scales
inversely with k_0. We discuss the extension to a system with a finite initial
charge density. The disorder averaged DC conductivity may be calculated by
adopting a technique developed for holographic lattices.
