On the local pairing behavior of critical points and roots of random polynomials

DOI10.1214/20-EJP499zbMath1451.30018arXiv1810.06781OpenAlexW3056585549MaRDI QIDQ2201472

Yanyan Li

Publication date: 29 September 2020

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.06781

zbMATH Keywords

zeroscritical pointsrandom polynomialsrandom Jordan curves

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Convergence of probability measures (60B10)

Related Items (4)

Free Convolution Powers Via Roots of Polynomials ⋮ Dynamics of Zeroes Under Repeated Differentiation ⋮ Almost sure behavior of the critical points of random polynomials ⋮ A nonlocal transport equation modeling complex roots of polynomials under differentiation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Erratum to: Outliers in the spectrum of iid matrices with bounded rank perturbations
• On the distribution of critical points of a polynomial
• Random matrices: universality of local eigenvalue statistics
• A generalization of the Lindeberg principle
• The converse of the Jordan curve theorem and a characterization of planar maps
• Relationship between the zeros of two polynomials
• Harmonic mean, random polynomials and stochastic matrices.
• Random matrices: universality of local spectral statistics of non-Hermitian matrices
• Pairing of zeros and critical points for random meromorphic functions on Riemann surfaces
• Spectra of nearly Hermitian random matrices
• Pairing of zeros and critical points for random polynomials
• Limiting empirical distribution of zeros and critical points of random polynomials agree in general
• A companion matrix approach to the study of zeros and critical points of a polynomial
• Distances between zeroes and critical points for random polynomials with i.i.d. zeroes
• The Distribution of Zeros of the Derivative of a Random Polynomial
• Saddle points in the chaotic analytic function and Ginibre characteristic polynomial
• Critical Points of Random Polynomials and Characteristic Polynomials of Random Matrices
• Pairing between zeros and critical points of random polynomials with independent roots
• Probability: A Graduate Course
• On a Converse of the Jordan Curve Theorem
• Advanced Probability Theory, Second Edition,
• A STABILITY VERSION OF THE GAUSS–LUCAS THEOREM AND APPLICATIONS
• Correlations and Pairing between Zeros and Critical Points of Gaussian Random Polynomials
• Local Universality of Zeroes of Random Polynomials
• Critical points of random polynomials with independent identically distributed roots
• An Inverse Matrix Adjustment Arising in Discriminant Analysis
• Optimal Transport

This page was built for publication: On the local pairing behavior of critical points and roots of random polynomials