# Difference between revisions of "Probability Seminar"

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== October 1, 2020, [https://marcusmichelen.org/ Marcus Michelen], [https://mscs.uic.edu/ UIC] == | == October 1, 2020, [https://marcusmichelen.org/ Marcus Michelen], [https://mscs.uic.edu/ UIC] == | ||

− | Title: ''' | + | Title: '''Roots of random polynomials near the unit circle''' |

− | Abstract: | + | 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. |

[[Past Seminars]] | [[Past Seminars]] |

## Revision as of 21:58, 28 August 2020

# Fall 2020

**Thursdays in 901 Van Vleck Hall at 2:30 PM**, unless otherwise noted.
**We usually end for questions at 3:20 PM.**

** IMPORTANT: ** In Fall 2020 the seminar is being run online.

If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu

## September 3, 2020, TBA (TBA)

**TBA**

## September 10, 2020,

## October 1, 2020, Marcus Michelen, UIC

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.