Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse Littlewood-Offord theorems and the condition number of random
  discrete matrices   Consider a random sum $\eta_1 v_1 + ... + \eta_n v_n$, where
$\eta_1,...,\eta_n$ are i.i.d. random signs and $v_1,...,v_n$ are integers. The
Littlewood-Offord problem asks to maximize concentration probabilities such as
$\P(\eta_1 v_1 + ... + \eta_n v_n = 0)$ subject to various hypotheses on the
$v_1,...,v_n$. In this paper we develop an \emph{inverse} Littlewood-Offord
theorem (somewhat in the spirit of Freiman's inverse sumset theorem), which
starts with the hypothesis that a concentration probability is large, and
concludes that almost all of the $v_1,...,v_n$ are efficiently contained in an
arithmetic progression. As an application we give some new bounds on the
distribution of the least singular value of a random Bernoulli matrix, which in
turn gives upper tail estimates on the condition number.

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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: astro-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: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: nlin