  We show that fluctuations of bulk operators that are restricted to some
region of space scale as the surface area of the region, independently of its
geometry. Specifically, we consider two point functions of operators that are
integrals over local operator densities whose two point functions falls off
rapidly at large distances, and does not diverge too strongly at short
distances. We show that the two point function of such bulk operators is
proportional to the area of the common boundary of the two spatial regions.
Consequences of this, relevant to the holographic principle and to area-scaling
of Unruh radiation are briefly discussed.
