Roots of random polynomials near the unit circle

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Combinatorics Seminar
April 8, 2021
10:20AM - 11:15AM
Location
Zoom

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Add to Calendar 2021-04-08 10:20:00 2021-04-08 11:15:00 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. Zoom Department of Mathematics math@osu.edu America/New_York public
Description

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.

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