Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Circular Law for Random Block Band Matrices with Genuinely Sublinear
  Bandwidth   We prove the circular law for a class of non-Hermitian random block band
matrices with genuinely sublinear bandwidth. Namely, we show there exists $\tau
\in (0,1)$ so that if the bandwidth of the matrix $X$ is at least $n^{1-\tau}$
and the nonzero entries are iid random variables with mean zero and slightly
more than four finite moments, then the limiting empirical eigenvalue
distribution of $X$, when properly normalized, converges in probability to the
uniform distribution on the unit disk in the complex plane. The key technical
result is a least singular value bound for shifted random band block matrices
with genuinely sublinear bandwidth, which improves on a result of Cook in the
band matrix setting.

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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
3
The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org