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We discuss the use of a lognormal (LN) random field as a model for the distribution of matter in the Universe. We find a number of reasons why this should be a plausible approximation to the distribution of density irregularities obtained by evolving from Gaussian initial conditions. Unlike straightforward linear theory, the model always has |0| but is arbitrarily close to the Gaussian at early times. It has the added advantage that, like the Gaussian model, all its statistical properties can be formulated in terms of one covariance function.
Coles et al. (1991) studied this question.