We study the number and distribution of limit cycles a planar vector field whose component functions are random polynomials. prove lower bound on average when polynomials sampled from Kostlan-Shub-Smale ensemble. Investigating problem introduced by Brudnyi [Ann. Math. (2) 154 (2001), pp. 227–243] we also consider special local setting counting near randomly perturbed center focus, perturbation ...