  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.
