Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Truncations of Haar distributed matrices, traces and bivariate Brownian
  bridges   Let U be a Haar distributed unitary matrix in U(n)or O(n). We show that after
centering the double index process $$ W^{(n)} (s,t) = \sum_{i \leq \lfloor ns
\rfloor, j \leq \lfloor nt\rfloor} |U_{ij}|^2 $$ converges in distribution to
the bivariate tied-down Brownian bridge. The proof relies on the notion of
second order freeness.

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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: q-bio