On the Relationship Between Correlation Length and Rate of Fluctuation of Random Fields

We show that the correlation length of a random field, modelled as a real wide-sense stationary stochastic process, defines a lower limit on the average squared rate of fluctuation of the field. For a sample-continuous process, the uncertainty relation between the correlation length and the spectral bandwidth exhibits a lower limit that depends explicitly on the selected correlation threshold level and implicitly on the functional form of the correlation function. We discuss implications of this result on how a selected correlation threshold relates to the estimated levels of field distortion and maximum amplitude of mode-stirred reverberation fields.