Measures with zeros in the inverse of their moment matrix
Probability
2009-09-29 v2 Statistics Theory
Statistics Theory
Abstract
We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure has zeros in some prescribed entries. We describe precisely which pattern of these zeroes corresponds to independence, namely, the measure having a product structure. A more refined finding is that the key factor forcing a zero entry in this inverse matrix is a certain conditional triangularity property of the orthogonal polynomials associated with .
Keywords
Cite
@article{arxiv.math/0702314,
title = {Measures with zeros in the inverse of their moment matrix},
author = {J. William Helton and Jean B. Lasserre and Mihai Putinar},
journal= {arXiv preprint arXiv:math/0702314},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/07-AOP365 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)