Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rates in the strong invariance principle for ergodic automorphisms of
  the torus   Let T be an ergodic automorphism of the d-dimensional torus. In the spirit of
Le Borgne, we give conditions on the Fourier coeffi cients of a real valued
function f under which the Birkhoff sums satis fy a strong invariance
principle. Next, reinforcing the condition on the Fourier coeffi cients in a
natural way, we obtain explicit rates of convergence in the strong invariance
principle.

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The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci