Statistical simulation of an exponentially correlated many-dimensional random field

A model of a many-dimensional homogeneous isotropic random field with an exponential correlation function and a given arbitrary one-dimensional distribution suitable for numerical implementation is constructed. The model is based on partition of the phase space by a field of random hyperplanes determined by some parametric Poisson point field. The possibility of application of this model to the solution of stochastic problems of radiation balance based on the combination of the methods of 'double randomization' and 'maximal section' is discussed.