Statistical properties of an isotropic random surface

Abstract

A number of statistical properties of a random, moving surface are obtained in the special case when the surface is Gaussian and isotropic. The results may be stated with special simplicity for a ‘ring' spectrum when the energy in the spectrum is confined to one particular wavelength y. In particular, the average density of maxima per unit area equals pie/(2/3y ² ), and the average length, per unit area, of the contour drawn at the mean level equals pie/(/2y)