Root separation in random polynomials

A classical result states that a random polynomial of large degree n with i.i.d. coefficients has most of its roots near the unit circle, approximately rotationally equidistributed. A key feature is that the random roots tend to “repel” one another. To quantify this repulsion, we study the minimal separation distance between roots, and show that when rescaled by n^{5/4}, it converges to a non-trivial limit law.

Based on a joint work with Marcus Michelen.