Abstract:
We give an explicit formula for the correlation functions of real zeros of a random polynomial with arbitrary independent continuously distributed coefficients.
Key words and phrases:random polynomial, correlation between zeros, joint intensities, Coarea formula.
The work was done with the financial support of the Bielefeld University (Germany) in terms of project SFB 701. The work of the third author is supported by the grant RFBR 16-01-00367 and by the Program of Fundamental Researches of Russian Academy of Sciences “Modern Problems of Fundamental Mathematics”.
Citation:
F. Götze, D. Koliada, D. Zaporozhets, “Correlation functions of real zeros of random polynomials”, Probability and statistics. Part 24, Zap. Nauchn. Sem. POMI, 454, POMI, St. Petersburg, 2016, 102–111; J. Math. Sci. (N. Y.), 229:6 (2018), 664–670
\Bibitem{GotKolZap16}
\by F.~G\"otze, D.~Koliada, D.~Zaporozhets
\paper Correlation functions of real zeros of random polynomials
\inbook Probability and statistics. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 454
\pages 102--111
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6386}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3602403}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 229
\issue 6
\pages 664--670
\crossref{https://doi.org/10.1007/s10958-018-3705-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042236225}
Linking options:
https://www.mathnet.ru/eng/znsl6386
https://www.mathnet.ru/eng/znsl/v454/p102
This publication is cited in the following 5 articles:
Marcus Michelen, Sean O'Rourke, “On random polynomials with an intermediate number of real roots”, Proc. Amer. Math. Soc., 152:11 (2024), 4933
Nguyen O., Vu V., “Roots of Random Functions: a Framework For Local Universality”, Am. J. Math., 144:1 (2022), 1–74
Oanh Nguyen, Van Vu, “Random polynomials: Central limit theorems for the real roots”, Duke Math. J., 170:17 (2021)
Yen Do, Van Vu, “Central limit theorems for the real zeros of Weyl polynomials”, Am. J. Math., 142:5 (2020), 1327–1369
F. Goetze, D. Koleda, D. Zaporozhets, “Joint distribution of conjugate algebraic numbers: a random polynomial approach”, Adv. Math., 359 (2020), 106849