Difference between revisions of "Probability Seminar"

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(Fall 2020)
(October 1, 2020, Marcus Michelen, UIC)
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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: '''TBA'''
+
Title: '''Roots of random polynomials near the unit circle'''
  
Abstract: TBA
+
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 20:58, 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.


Past Seminars