Consider a random system f1(x)=0,…,fn(x)=0 of
n random real polynomials in n variables, where each fk has a
prescribed set of exponent vectors in a set Ak⊆Zn of size
tk. Assuming that the coefficients of the fk are independent
Gaussian of any variance, we prove that the expected number of zeros of the
random system in the positive orthant is bounded from above by 4−n∏k=1ntk(tk−1). This result is a probabilisitc version of
Kushnirenko's conjecture; it provides a bound that only depends on the number
of terms and is independent of their degree.Comment: 26 pages. Different original titl