Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal eigenvector correlations in quaternionic Ginibre ensembles   Non-Hermitian random matrices enjoy non-trivial correlations in the
statistics of their eigenvectors. We study the overlap among left and right
eigenvectors in Ginibre ensembles with quaternion valued Gaussian matrix
elements. This concept was introduced by Chalker and Mehlig in the complex
Ginibre ensemble. Using a Schur decomposition, for harmonic potentials we can
express the overlap in terms of complex eigenvalues only, coming in conjugate
pairs in this symmetry class. Its expectation value leads to a Pfaffian
determinant, for which we explicitly compute the matrix elements for the
induced Ginibre ensemble with $2\alpha$ zero eigenvalues, for finite matrix
size $N$. In the macroscopic large-$N$ limit in the bulk of the spectrum we
recover the limiting expressions of the complex Ginibre ensemble for the
diagonal and off-diagonal overlap, which are thus universal.

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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: atom-ph