Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High Probability Analysis of the Condition Number of Sparse Polynomial
  Systems   Let F:=(f_1,...,f_n) be a random polynomial system with fixed n-tuple of
supports. Our main result is an upper bound on the probability that the
condition number of f in a region U is larger than 1/epsilon. The bound depends
on an integral of a differential form on a toric manifold and admits a simple
explicit upper bound when the Newton polytopes (and underlying covariances) are
all identical.
  We also consider polynomials with real coefficients and give bounds for the
expected number of real roots and (restricted) condition number. Using a Kahler
geometric framework throughout, we also express the expected number of roots of
f inside a region U as the integral over U of a certain {\bf mixed volume}
form, thus recovering the classical mixed volume when U = (C^*)^n.

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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin