Summary: On the roots of a random system of equations.
The theorem of Shub & Smale and some
August 20, 2004
We give a new proof of a theorem of Shub & Smale  on the
expectation of the number of roots of a system of m random polyno-
mial equations in m real variables, having a special isotropic Gaussian
distribution. Further, we present a certain number of extensions, in-
cluding the behaviour as m + of the variance of the number of
roots, when the system of equations is also stationary.
AMS subject classification: Primary 60G60, 14Q99. Secondary: 30C15.
Short Title: Random systems
Key words and phrases: Random polynomials, system of random equa-
tions, Rice Formula.