Asymptotic variance and CLT for the number of zeros of Kostlan Shub Smale random polynomials

DOI10.1016/j.crma.2015.09.016zbMath1331.60046arXiv1504.05355OpenAlexW1879379973MaRDI QIDQ5965098

Federico Dalmao

Publication date: 2 March 2016

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.05355

zbMATH Keywords

Kostlan-Shub-Smale random polynomials

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stochastic processes (60G99) Real polynomials: location of zeros (26C10)

Related Items (9)

A CLT concerning critical points of random functions on a Euclidean space ⋮ An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process ⋮ Variance of the volume of random real algebraic submanifolds II ⋮ Asymptotic variance of the number of real roots of random polynomial systems ⋮ Zeros of smooth stationary Gaussian processes ⋮ Random polynomials: central limit theorems for the real roots ⋮ Real roots of random polynomials with coefficients of polynomial growth: a comparison principle and applications ⋮ Roots of Kostlan polynomials: moments, strong law of large numbers and central limit theorem ⋮ Variance of the volume of random real algebraic submanifolds

Cites Work

• CLT for crossings of random trigonometric polynomials
• Real roots of random polynomials and zero crossing properties of diffusion equation
• Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: Crossings and extremes
• On the Kostlan-Shub-Smale model for random polynomial systems. Variance of the number of roots
• Level Sets and Extrema of Random Processes and Fields
• On the Distribution of the Number of Real Roots of Random Polynomials
• Distribution of roots of random polynomials
• Central limit theorems for level functionals of stationary Gaussian processes and fields
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Asymptotic variance and CLT for the number of zeros of Kostlan Shub Smale random polynomials