Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Research & business

Research lectures, seminars and events

The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but  wish to enquire about attending one of the events please contact the organiser or host department.


 

Probability Seminar: Roots of random polynomials near the unit circle

Presented by Marcus Michelen, University of Illinois
30 October 2020 13:00 in Zoom

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.

Contact ellen.g.powell@durham.ac.uk for more information