Zeros of random polynomials and their higher derivatives
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- by Sung-Soo Byun, Jaehun Lee and Tulasi Ram Reddy PDF
- Trans. Amer. Math. Soc. 375 (2022), 6311-6335 Request permission
Abstract:
We consider zeros of higher derivatives of various random polynomials and show that their limiting empirical measures agree with those of roots of corresponding random polynomials. Examples of random polynomials include those whose roots are given by i.i.d. random variables and those whose zeros are nearly all deterministic except for a fixed number of random roots. As an application, we show that such a phenomenon holds for the random polynomials whose roots follow the distribution of the 2D Coulomb gas ensemble.References
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Additional Information
- Sung-Soo Byun
- Affiliation: School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, Republic of Korea
- MR Author ID: 1329254
- ORCID: 0000-0002-2405-2089
- Email: sungsoobyun@kias.re.kr
- Jaehun Lee
- Affiliation: School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, Republic of Korea
- MR Author ID: 1303252
- ORCID: 0000-0002-6726-6044
- Email: hun618@snu.ac.kr
- Tulasi Ram Reddy
- Affiliation: Deutsche Bank, Mumbai, India
- MR Author ID: 1144801
- ORCID: setImmediate$0.28992355038398343$6
- Email: tulasi.math@gmail.com
- Received by editor(s): February 5, 2018
- Received by editor(s) in revised form: January 20, 2022, and January 20, 2022
- Published electronically: June 30, 2022
- Additional Notes: The first author was partially supported by Samsung Science and Technology Foundation (SSTF-BA1401-51), by the National Research Foundation of Korea (NRF-2019R1A5A1028324) and partially through IRTG 2235
The second author was supported by a KIAS Individual Grant (MG079301) at Korea Institute for Advanced Study and partially through IRTG 2235
All the work was done when the third author was a post-doctoral researcher in New York University, Abu Dhabi - © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 375 (2022), 6311-6335
- MSC (2020): Primary 60G99; Secondary 30C15
- DOI: https://doi.org/10.1090/tran/8674
- MathSciNet review: 4474893