Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Concentration of the mixed discriminant of well-conditioned matrices   We call an n-tuple Q_1, ..., Q_n of positive definite nxn matrices
alpha-conditioned for some alpha > 1 if the ratio of the largest among the
eigenvalues of Q_1, ..., Q_n to the smallest among the eigenvalues of Q_1, ...,
Q_n does not exceed alpha. An n-tuple is called doubly stochastic if the sum of
Q_i is the identity matrix and the trace of each Q_i is 1. We prove that for
any fixed alpha > 1 the mixed discriminant of an alpha-conditioned doubly
stochastic n-tuple is n^{O(1)} e^{-n}. As a corollary, for any alpha > 1 fixed
in advance, we obtain a polynomial time algorithm approximating the mixed
discriminant of an alpha-conditioned n-tuple within a polynomial in n factor.

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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
28
The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga