We develop a technique for the construction of random fields on algebraic structures. We deal with two general situations: random fields on homogeneous spaces of a compact group and in the spin line bundles of the 2-sphere. In particular, every complex Gaussian isotropic spin random field can be...

We prove a functional central limit theorem for the Hausdorff measure of level sets generated by a smooth Gaussian random field.

Motivated by the papers of Choi (2010) and Pereira (2010), in this work, we proved two limit theorems for the maxima of Gaussian fields. First, a Cox limit theorem is established for a stationary strongly dependent Gaussian random field. Second, a Gumbel type extreme limit theorem is proved for...

Consider a stationary Gaussian random field on Rd with spectral density f(λ) that satisfies f(λ)∼c|λ|−θ as |λ|→∞. The parameters c and θ control the tail behavior of the spectral density. c is related to a microergodic parameter and θ is related to a fractal index. For data...