Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Yeager, Aaron"'
We utilize Cauchy's argument principle in combination with the Jacobian of a holomorphic function in several complex variables and the first moment of a ratio of two correlated complex normal random variables to prove explicit formulas for the densit
Externí odkaz:
http://arxiv.org/abs/2108.09687
Publikováno v:
Involve 14 (2021) 271-281
We study the expected number of zeros of $$P_n(z)=\sum_{k=0}^n\eta_kp_k(z),$$ where $\{\eta_k\}$ are complex-valued i.i.d standard Gaussian random variables, and $\{p_k(z)\}$ are polynomials orthogonal on the unit disk. When $p_k(z)=\sqrt{(k+1)/\pi}
Externí odkaz:
http://arxiv.org/abs/2007.03445
Autor:
Yeager, Aaron M.
Let $\{\varphi_k\}_{k=0}^\infty $ be a sequence of orthonormal polynomials on the unit circle (OPUC) with respect to a probability measure $ \mu $. We study the variance of the number of zeros of random linear combinations of the form $$ P_n(z)=\sum_
Externí odkaz:
http://arxiv.org/abs/1908.02234
Autor:
Yeager, Aaron M.
Let $\{f_k\}$ be a sequence of entire functions that are real valued on the real-line. We study the expected number of real zeros of random sums of the form $P_n(z)=\sum_{k=0}^n\eta_k f_k(z)$, where $\{\eta_k\}$ are real valued i.i.d.~random variable
Externí odkaz:
http://arxiv.org/abs/1903.06642
Autor:
Yeager, Aaron
Let $\{f_j\}_{j=0}^n$ be a sequence of orthonormal polynomials where the orthogonality relation is satisfied on either the real line or on the unit circle. We study zero distribution of random linear combinations of the form $$P_n(z)=\sum_{j=0}^n\eta
Externí odkaz:
http://arxiv.org/abs/1711.11178
Autor:
Yattselev, Maxim L., Yeager, Aaron
Publikováno v:
Indiana Univ. Math. J, 68(3), 835-856, 2019
Let \( \{\varphi_i\}_{i=0}^\infty \) be a sequence of orthonormal polynomials on the unit circle with respect to a probability measure \( \mu \). We study zero distribution of random linear combinations of the form \[ P_n(z)=\sum_{i=0}^{n-1}\eta_i\va
Externí odkaz:
http://arxiv.org/abs/1711.07852
Autor:
Yeager, Aaron M.
We study zero distribution of random linear combinations of the form $$P_n(z)=\sum_{j=0}^n\eta_j\phi_j(z),$$ in any Jordan region $\Omega \subset \mathbb C$. The basis functions $\phi_j$ are orthogonal polynomials on the unit circle (OPUC) that are r
Externí odkaz:
http://arxiv.org/abs/1608.02805
Autor:
Yeager, Aaron
We study zero distribution of random linear combinations of the form $$P_n(z)=\sum_{j=0}^n\eta_jf_j(z),$$ in any Jordan region $\Omega \subset \mathbb C$. The basis functions $f_j$ are entire functions that are real-valued on the real line, and $\eta
Externí odkaz:
http://arxiv.org/abs/1605.06836
Autor:
Pritsker, Igor E., Yeager, Aaron M.
Zeros of many ensembles of polynomials with random coefficients are asymptotically equidistributed near the unit circumference. We give quantitative estimates for such equidistribution in terms of the expected discrepancy and expected number of roots
Externí odkaz:
http://arxiv.org/abs/1407.6769
Autor:
Yattselev, Maxim L., Yeager, Aaron
Publikováno v:
Indiana University Mathematics Journal, 2019 Jan 01. 68(3), 835-856.
Externí odkaz:
https://www.jstor.org/stable/26769444
