Disks as Inhomogeneous, Anisotropic Gaussian Random Fields

Understand

We model astrophysical disk surface brightness fluctuations as an inhomogeneous, anisotropic, time-dependent Gaussian random field.

• The field locally obeys the stochastic partial differential equation of a Mat\'ern field, which has a power spectrum that is flat at large scales and falls off as a power law at small scales.
• We provide a series of pedagogical examples and along the way provide a convenient parameterization for the local covariance.
• We then consider two applications to disks.