Harmonic mean, random polynomials and stochastic matrices
概率论
2007-05-23 v2 机器学习
经典分析与常微分方程
组合数学
动力系统
摘要
Motivated by a problem in learning theory, we are led to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the derivative of random polynomials (generated by picking their roots uniformly at random in the interval [0, 1], although our results extend to other distributions). This, in turn, requires the study of the statistical behavior of the harmonic mean of random variables as above, and that, in turn, leads us to delicate question of the rate of convergence to stable laws and tail estimates for stable laws.
引用
@article{arxiv.math/0105236,
title = {Harmonic mean, random polynomials and stochastic matrices},
author = {Natalia Komarova and Igor Rivin},
journal= {arXiv preprint arXiv:math/0105236},
year = {2007}
}