English

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 μ\mu 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 μ\mu.

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)