Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anomalous singularity of the solution of the vector Dyson equation in
  the critical case   We consider the solution of the vector Dyson equation $-1/m=z+Sm$ in the case
when $S$ has a block staircase structure with $(n-1)$ different critical zero
blocks below the strictly positive anti-diagonal and all elements right above
the anti-diagonal are strictly positive. We prove that the components of $m$
behave as fractional powers of $z$ in the neighbourhood of zero and show that
the self-consistent density of states $\rho(E)$ behaves as $\vert
E\vert^{-\frac{n-1}{n+1}}$ as $E$ tends to zero, where $n^2$ is a number of
blocks. Both constant block and non-constant block cases are considered. In the
non-constant case uniform estimates for the components of $m$ are obtained.

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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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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: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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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: supr-con