On Zeroes of Random Polynomials and an Application to Unwinding
Publication
, Journal Article
Steinerberger, S; Wu, HT
Published in: International Mathematics Research Notices
July 1, 2021
Let μ be a probability measure in C with a continuous and compactly supported density function, let z1, zn be independent random variables, zi ∼ μ, and consider the random polynomial pn(z) = ∏ k=1n(z-zk).We determine the asymptotic distribution of left z C: pn(z) = pn(0). In particular, if mu is radial around the origin, then those solutions are also distributed according to mu as n. Generally, the distribution of the solutions will reproduce parts of mu and condense another part on curves. We use these insights to study the behavior of the Blaschke unwinding series on random data.
Duke Scholars
Published In
International Mathematics Research Notices
DOI
EISSN
1687-0247
ISSN
1073-7928
Publication Date
July 1, 2021
Volume
2021
Issue
13
Start / End Page
10100 / 10117
Related Subject Headings
- General Mathematics
- 4902 Mathematical physics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Steinerberger, S., & Wu, H. T. (2021). On Zeroes of Random Polynomials and an Application to Unwinding. International Mathematics Research Notices, 2021(13), 10100–10117. https://doi.org/10.1093/imrn/rnz096
Steinerberger, S., and H. T. Wu. “On Zeroes of Random Polynomials and an Application to Unwinding.” International Mathematics Research Notices 2021, no. 13 (July 1, 2021): 10100–117. https://doi.org/10.1093/imrn/rnz096.
Steinerberger S, Wu HT. On Zeroes of Random Polynomials and an Application to Unwinding. International Mathematics Research Notices. 2021 Jul 1;2021(13):10100–17.
Steinerberger, S., and H. T. Wu. “On Zeroes of Random Polynomials and an Application to Unwinding.” International Mathematics Research Notices, vol. 2021, no. 13, July 2021, pp. 10100–17. Scopus, doi:10.1093/imrn/rnz096.
Steinerberger S, Wu HT. On Zeroes of Random Polynomials and an Application to Unwinding. International Mathematics Research Notices. 2021 Jul 1;2021(13):10100–10117.
Published In
International Mathematics Research Notices
DOI
EISSN
1687-0247
ISSN
1073-7928
Publication Date
July 1, 2021
Volume
2021
Issue
13
Start / End Page
10100 / 10117
Related Subject Headings
- General Mathematics
- 4902 Mathematical physics
- 0101 Pure Mathematics