Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Sparse Polynomial Systems   Let f:=(f^1,\...,f^n) be a sparse random polynomial system. This means that
each f^i has fixed support (list of possibly non-zero coefficients) and each
coefficient has a Gaussian probability distribution of arbitrary variance.
  We express the expected number of roots of f inside a region U as the
integral over U of a certain mixed volume form. When U = (C^*)^n, the classical
mixed volume is recovered.
  The main result in this paper is a bound on the probability that the
condition number of f on the region U is larger than 1/epsilon. This bound
depends on the integral of the mixed volume form over U, and on a certain
intrinsic invariant of U as a subset of a toric manifold.
  Polynomials with real coefficients are also considered, and bounds for the
expected number of real roots and for the condition number are given.
  The connection between zeros of sparse random polynomial systems, Kahler
geometry, and mechanics (momentum maps) is discussed.

27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph