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On the distribution of critical points of a polynomial


 
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1. Title Title of document On the distribution of critical points of a polynomial
 
2. Creator Author's name, affiliation, country Sneha Dey Subramanian; University of Pennsylvania; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) critical points; random polynomials; Pemantle-Rivin conjecture
 
3. Subject Subject classification 60G99
 
4. Description Abstract

This paper proves that if points $Z_1,Z_2,...$ are chosen independently and identically using some measure $\mu$ from the unit circle in the complex plane, with $p_n(z) = (z-Z_1)(z-Z_2)...(z-Z_n)$, then the empirical distribution of the critical points of $p_n$ converges weakly to $\mu$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2012-08-26
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2040
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-2040
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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