Random systems of polynomial equations. The expected number of roots under smooth analysis

Diego Armentano, Mario Wschebor

We consider random systems of equations over the reals, with $m$ equations and $m$ unknowns $P_i(t)+X_i(t)=0$, $t\in {\mathbb{R}}^m$, $i=1,...,m$, where the $P_i$'s are non-random pol…