Roots of random polynomials near the unit circle

Speaker:  Marcus Michelen (University of Illinois at Chicago)

Title:  Roots of random polynomials near the unit circle

Abstract:  It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle.

Based on joint work with Julian Sahasrabudhe.