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Representation of Gaussian isotropic spin random fields

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  • Baldi, Paolo
  • Rossi, Maurizia

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. Lévy’s original idea for the spherical Brownian motion.

Suggested Citation

  • Baldi, Paolo & Rossi, Maurizia, 2014. "Representation of Gaussian isotropic spin random fields," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1910-1941.
  • Handle: RePEc:eee:spapps:v:124:y:2014:i:5:p:1910-1941
    DOI: 10.1016/j.spa.2014.01.007
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    References listed on IDEAS

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    1. Baldi, Paolo & Marinucci, Domenico, 2007. "Some characterizations of the spherical harmonics coefficients for isotropic random fields," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 490-496, March.
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    Cited by:

    1. Chunsheng Ma & Anatoliy Malyarenko, 2020. "Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous Spaces," Journal of Theoretical Probability, Springer, vol. 33(1), pages 319-339, March.
    2. Cleanthous, Galatia & Georgiadis, Athanasios G. & Lang, Annika & Porcu, Emilio, 2020. "Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4873-4891.

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