On the Number of Real Zeros of Random Fewnomials

Consider a system $f_1(x)=0,\dots ,f_n(x)=0$ of $n$ random real polynomials in $n$ variables, where each $f_i$ has a prescribed set of terms described by a set $A\subseteq {\mathbb{N}}^n$ of cardinality $t$. Assuming that the coefficients of the $f_i$ are independent Gaussians of any variance, we prove that the expected number of zeros of the random system in the positive orthant is bounded from above by $\frac{1}{2^{n-1}}\left(\genfrac{}{}{0px}{}{t}{n}\right)$.