Analysis-Combinatorics Joint Seminar: Sums of random polynomials with independent roots

Abstract:  We consider the sum of independent random polynomials as their degrees tend to infinity.  Namely, let $p$ and $q$ be two independent random polynomials of degree $n$, whose roots are chosen independently in the complex plane. We compute the limiting distribution for the zeros of the sum $p+q$ as $n$ tends to infinity by analyzing its logarithmic potential.  We will also discuss a generalization for more than two polynomials.  These results can be viewed as describing a version of the free additive convolution from free probability theory for zeros of polynomials. The talk is based on joint work with Tulasi Ram Reddy.