Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sample covariance matrices and special symmetric partitions   Suppose $X_p$ is a real $p \times n$ matrix with independent entries and
consider the (unscaled) sample covariance matrix $S_p=X_pX_p^T$. The
Marchenko-Pastur law was discovered as the limit of the bulk distribution of
the sample covariance matrix in 1967. There have been extensions of this result
in several directions. In this paper, we consider an extension that handles
several of the existing ones as well as generates new results.
  We show that under suitable assumptions on the entries of $X_p$, the limiting
spectral distribution exists in probability or almost surely. The moments are
described by a set of partitions that are beyond pair partitions and
non-crossing partitions and are also related to special symmetric partitions,
which are known to appear in the limiting spectral distribution of Wigner-type
matrices. Similar results hold for other patterned matrices such as reverse
circulant, circulant, Toeplitz, and Hankel matrices.

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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: q-alg