Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Universality of the Non-singularity of General Ginibre and Wigner
  Random Matrices   We prove the universal asymptotically almost sure non-singularity of general
Ginibre and Wigner ensembles of random matrices when the distribution of the
entries are independent but not necessarily identically distributed and may
depend on the size of the matrix. These models include adjacency matrices of
random graphs and also sparse, generalized, universal and banded random
matrices. We find universal rates of convergence and precise estimates for the
probability of singularity which depend only on the size of the biggest jump of
the distribution functions governing the entries of the matrix and not on the
range of values of the random entries. Moreover, no moment assumptions are made
about the distributions governing the entries. Our proofs are based on a
concentration function inequality due to Kolmogorov, Rogozin and Kesten, which
allows us to improve universal rates of convergence for the Wigner case when
the distribution of the entries do not depend on the size of the matrix.

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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: physics