An asymptotic expansion for the expected number of real zeros of Kac–Geronimus polynomials
نویسندگان
چکیده
Let {φi(z;α)}i=0∞, corresponding to α∈(−1,1), be orthonormal Geronimus polynomials. We study asymptotic behavior of the expected number real zeros, say
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Article history: Received 28 April 2015 Accepted after revision 17 September 2015 Available online 29 October 2015 Presented by the Editorial Board In this note, we find the asymptotic main term of the variance of the number of roots of Kostlan–Shub–Smale random polynomials and prove a central limit theorem for this number of roots as the degree goes to infinity. © 2015 Académie des sciences. P...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2021
ISSN: ['0035-7596', '1945-3795']
DOI: https://doi.org/10.1216/rmj.2021.51.1171