Abstract
Gaussian processes are defined by their means and covariances. The covariance matrix of a stationary process is a convolution operator that is diagonalized in the Fourier basis. Its eigenvalues define the spectral power of the process.
Multiscale processes have long-range covariances, characterized by a spectral power that decreases in a power law. This covariance can be represented with a wavelet transform, which separates the dyadic scales. Non-Gaussian processes are characterized by variations at different scales that are not independent, although they are uncorrelated when the process is stationary. Maximum entropy models of physical fields are obtained by eliminating the complex phase and correlating the moduli of the wavelet coefficients. The maximum entropy models calculated from these moments can be used to generate complex physical fields. This is illustrated on the mass distribution of the universe on the cosmic web, and turbulent fluid fields.
