Sums of random polynomials with independent roots

We consider the zeros of sum independent random polynomials as their degrees tend to infinity. Namely, let p and q be two degree n, whose roots are chosen independently from probability measures μ ν in complex plane, respectively. compute limiting distribution for p+q n tends The can described by its logarithmic potential, which we show is pointwise maximum potentials ν. More generally, m when fixed Our results viewed describing a version free additive convolution theory polynomials.