Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stein's method and the multivariate CLT for traces of powers on the
  classical compact groups   Let $M_n$ be a random element of the unitary, special orthogonal, or unitary
symplectic groups, distributed according to Haar measure. By a classical result
of Diaconis and Shahshahani, for large matrix size $n$, the vector $
(\on{Tr}(M_n), \on{Tr}(M_n^2),..., \on{Tr}(M_n^d))$ tends to a vector of
independent (real or complex) Gaussian random variables. Recently, Jason Fulman
has demonstrated that for a single power $j$ (which may grow with $n$), a speed
of convergence result may be obtained via Stein's method of exchangeable pairs.
In this note, we extend Fulman's result to the multivariate central limit
theorem for the full vector of traces of powers.

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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: stat