The theory of space-dependent stochastic fluctuations is applied to several specific geometries to illustrate the space-dependence of the correlation and spectral-density functions. One-energy-group diffusion theory is used throughout to avoid clouding the geometric effects with other effects and to simplify the calculations. The first calculations are made in the infinite medium. The resulting cross-correlation and cross-spectral-density functions are shown to yield auto-correlation and spectral-density functions which differ strikingly from the usual point-reactor result. It is shown, however, that the point-reactor result is identical to the result obtained in an infinite reactor with a uniformly distributed detector. The effect of boundaries upon the fluctuations is examined from both the point of view of a finite detector and systems involving one or more boundaries. The case of the unreflected homogenous cubical reactor is solved. The results of cross-correlation and spectral-density calculations are displayed. The special case of the auto-correlation and spectral-density functions is compared to the point-reactor or space-independent result to show that significant departure from space independence is to be expected if detectors are placed away from axes of symmetry. This latter result obtains even when the extraneous source distribution is assumed to be fundamental mode.