April 8, 2021
10:20AM - 11:15AM
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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
OSU ASC Drupal 8
ascwebservices@osu.edu
America/New_York
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Date Range
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
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.
