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 represented in this way. Our construction extends P. Ldvy's original idea for the spherical Brownian motion
Baldi, P., Rossi, M. (2014). Representation of Gaussian isotropic spin random fields. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 124(5), 1910-1941 [10.1016/j.spa.2014.01.007].
Representation of Gaussian isotropic spin random fields
Rossi, Maurizia
2014
Abstract
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 represented in this way. Our construction extends P. Ldvy's original idea for the spherical Brownian motion
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