Edwards-Wilkinson surface over a spherical substrate: $1\mathrm{/}f$ noise in the height fluctuations

We study the steady state fluctuations of an Edwards-Wilkinson type surface with the substrate taken to be a sphere. We show that the height fluctuations on circles at a given latitude has the effective action of a perfect Gaussian $1\mathrm{/}f$ noise, just as in the case of fixed radius circles on an infinite planar substrate. The effective surface tension, which is the overall coefficient of the action, does not depend on the latitude angle of the circles.