Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multilevel Representations of Isotropic Gaussian Random Fields on the
  Sphere   Series expansions of isotropic Gaussian random fields on $\mathbb{S}^2$ with
independent Gaussian coefficients and localized basis functions are
constructed. Such representations provide an alternative to the standard
Karhunen-Lo\`eve expansions of isotropic random fields in terms of spherical
harmonics. Their multilevel localized structure of basis functions is
especially useful in adaptive algorithms. The basis functions are obtained by
applying the square root of the covariance operator to spherical needlets.
Localization of the resulting covariance-dependent multilevel basis is shown
under decay conditions on the angular power spectrum of the random field. In
addition, numerical illustrations are given and an application to random
elliptic PDEs on the sphere is analyzed.

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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: stat