It is well known that a random polynomial with iid coefficients has most of its roots close to the unit circle. Recently, we found that both the minimum modulus of the polynomial on the unit circle itself, as well as the closest root to the unit circle has a limiting exponential distribution. In the talk I will explain the joint mechanism behind these results.

The talk is based on joint works with Nicholas Cook, Hoi Nguyen and Ofer Zeitouni.

Recording of the talk can be found at

https://youtu.be/bFT8TpUVmEw