Anisotropic scaling of the random grain model

I will present anisotropic scaling limits of the random grain model on the plane with heavy-tailed grain area distribution. They have either independent or completely dependent increments along one or both coordinate axes and include stable, Gaussian and 'intermediate' infinitely divisible random fields. I will also give the asymptotic form of the covariance function of the random grain model and present some applications to superposed network traffic. The talk is based on a joint work with Donatas Surgailis (Vilnius University, Lithuania).