  The statistical properties of patch electric fields due to a polycrystalline
metal surface are calculated. The fluctuations in the electric field scale like
1/z^2, when z >> w, where z is the distance to the surface, and w is the
characteristic length scale of the surface patches. For typical thermally
evaporated gold surfaces these field fluctuations are comparable to the image
field of an elementary charge, and scale in the same way with distance to the
surface. Expressions for calculating the statistics of the inhomogeneous
broadening of Rydberg atom energies due to patch electric fields are presented.
Spatial variations in the patch fields over the Rydberg orbit are found to be
insignificant.
