  The lateral diffusion coefficient of a Brownian particle on a two-dimensional
random surface is studied in the quenched limit for which the surface
configuration is time-independent. We start with the stochastic equation of
motion for a Brownian particle on a fluctuating surface, which has been derived
by Naji and Brown. The mean square displacement of the particle projected on a
base plane is calculated exactly under the condition that the surface with a
constant shape has no spatial correlation. We prove that the obtained lateral
diffusion coefficient is in between the known upper and lower bounds.
