Harmonic mean, random polynomials and stochastic matrices

2001/05/29 by Natalia L. Komarova, Natalia Komarova, Komarova, Natalia +2 · 2 citations
Computer Science · Mathematics · #Algorithms and Data Compression #Bayesian Methods and Mixture Models #Neural Networks and Applications #cs.LG #math.CA #math.CO #math.DS #math.PR #msc:26C10 #msc:60E07 #msc:60F15 #msc:60J20 #msc:91E40

paper · pdf · doi:10.48550/arxiv.math/0105236

arxiv created 2001/12/03 · arxiv updated 2009/11/30

Abstract

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.

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