Low‐frequency electron density fluctuations of a bounded homogeneous plasma are determined at large wavelengths. It is shown that, when the wavelengths are large, the frequency spectrum of fluctuation is determined by the mean square displacement of an electron in a time intervalt, ⟨&Dgr;(t)2⟩. Using a Brownian motion model for ⟨&Dgr;(t)2⟩ which is exact at larget(as well as at smallt), the frequency spectrum can then be evaluated by the method of steepest descents. The resulting spectrum is exact at zero frequency and provides a method for local measurements of diffusion cofficients by light scattering or direct probe measurement techniques. The results are valid regardless of the number of particles in a Debye sphere or of the extent of ionization.