2020
DOI: 10.48550/arxiv.2003.13486
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The Turning Arcs: a Computationally Efficient Algorithm to Simulate Isotropic Vector-Valued Gaussian Random Fields on the $d$-Sphere

Abstract: Random fields on the sphere play a fundamental role in the natural sciences. This paper presents a simulation algorithm parenthetical to the spectral turning bands method used in Euclidean spaces, for simulating scalar-or vector-valued Gaussian random fields on the d-dimensional unit sphere. The simulated random field is obtained by a sum of Gegenbauer waves, each of which is variable along a randomly oriented arc and constant along the parallels orthogonal to the arc. Convergence criteria based on the Berry-E… Show more

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